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Measurement of the modified TG43 parameters for the bare S7600 Xoft Axxent source model

  • Autumn E. Walter
    Correspondence
    Corresponding author. Department of Human Oncology, School of Medicine and Public Health, University of Wisconsin, 1111 Highland Ave B1002, Madison, WI 53705, Tel.: (216) 870-3113.
    Affiliations
    Department of Medical Physics, School of Medicine and Public Health, University of Wisconsin, Madison, WI

    Department of Human Oncology, School of Medicine and Public Health, University of Wisconsin, Madison, WI
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  • Ahtesham U. Khan
    Affiliations
    Department of Medical Physics, School of Medicine and Public Health, University of Wisconsin, Madison, WI
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  • Larry A. DeWerd
    Affiliations
    Department of Medical Physics, School of Medicine and Public Health, University of Wisconsin, Madison, WI
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Open AccessPublished:January 07, 2023DOI:https://doi.org/10.1016/j.brachy.2022.11.010

      ABSTRACT

      PURPOSE

      The purpose of this work is to provide measured data for the modified TG43 parameters [DeWerd et al.] for the newest, Galden-cooled S7600 Xoft Axxent source model.

      METHODS

      The measurement of radial dose distributions at distances of 1 cm to 4 cm from the source was performed using TLD100 microcubes, EBT3 film, and an Exradin A26 microionization chamber. The overall uncertainty and reproducibility of each dosimeter was evaluated for its use in determining the radial dose function and dose rate conversion coefficient. An acrylic phantom developed in house for previous works was used to measure the polar anisotropy function using TLD100 microcubes at distances of 1 cm, 2 cm, and 5 cm from the source.

      RESULTS

      The Exradin A26 chamber was deemed most suitable for measuring the radial dose function. Values determined had a maximum k = 1 uncertainty of 1.4%. The dose rate conversion coefficient measured with the chamber was found to be 9.33 ± 0.21cGy/hrμGy/min. TLD100 microcube measurements of the polar anisotropy had average uncertainties of 6%, 3%, and 2.5% at 1 cm, 2 cm, and 5 cm, respectively.

      CONCLUSIONS

      The modified TG43 parameters for the bare source were measured with reasonable uncertainty. The values determined will aid with the clinical implementation of the source for breast and endometrial cancer applications.

      Keywords

      Introduction

      The Xoft Axxent electronic brachytherapy (eBt) source is a miniature x-ray tube that operates between 40 and 50 kVp. The x-ray tube and associated electronics of these sources are encased in a plastic cooling catheter which allows for a coolant to circulate around the anode. The older source model with series number S7500 has traditionally been cooled with water (

      Xoft, “Operator manual axxent controller model 110 rev. X.” 2013.

      ,
      • Eaton DJ
      Electronic brachytherapy-current status and future directions.
      ). There has recently been a shift to cooling these sources with the fluorocarbon liquid, Galden, which has a density of 1.72 g/cc (

      Solvay speciality polymers, “Galden HT PFPE heat transfer fluids” 2020, [Online]. Available: http://www.behlke.com/pdf/datasheets/galden_ht135.pdf (Accessed August 2019).

      ). These sources, denoted by the series number S7600, are expected to have a longer lifespan due to this new coolant, an increased thickness of the anode coating, and a change of the catheter material outside of the anode region to improve resistance to radiation damage.
      While these sources are similar to the older, S7500 series sources, these small changes can have an impact dosimetrically. As noted by Walter et al. (
      • Walter AE
      • Hull JL
      • DeWerd LA
      Comparison of air kerma rate between the S7500 and S7600 Xoft Axxent sources.
      ), the introduction of these changes caused a reduced air kerma rate at 50 cm from the source as well as an increase in the average energy of the source. There was a significant reduction in air kerma rate of approximately 17% due to the self-filtration caused by the increased anode thickness and beam hardening by the new coolant. Thus, it is important to further dosimetrically characterize these sources (
      • Walter AE
      • Hull JL
      • DeWerd LA
      Comparison of air kerma rate between the S7500 and S7600 Xoft Axxent sources.
      ).
      Previously, the formalism proposed in the AAPM Task Group 43 report and subsequent updates was used to determine dose rate in water from eBt sources (
      • Nath R
      • Anderson LL
      • Luxton G
      • et al.
      Dosimetry of interstitial brachytherapy sources: recommendations of the AAPM radiation therapy committee task group no. 43.
      ,
      • Rivard MJ
      • Coursey BM
      • DeWerd LA
      • et al.
      Update of AAPM task group no. 43 report: a revised AAPM protocol for brachytherapy dose calculations.
      ). However, in 2015 DeWerd et al. proposed a modification to this formalism such that it could be used for eBt sources (
      • DeWerd LA
      • Culberson WS
      • Micka JA
      • Simiele SJ
      A modified dose calculation formalism for electronic brachytherapy sources.
      ). In particular, this formalism accounts for fluctuations in dose rate of the sources by shifting to an air-kerma rate standard measured at 50 cm from the source. Additionally, it accounts for any bremsstrahlung perturbation from the various applicators used for intracavitary brachytherapy applications. This modified formalism defines the dose rate in water as (
      • DeWerd LA
      • Culberson WS
      • Micka JA
      • Simiele SJ
      A modified dose calculation formalism for electronic brachytherapy sources.
      ),
      D˙i(r,θ)=K˙50cm·χi(1cm,π2)·GP(r,θ0)GP(r0,θ0)·gi(r,θ)·Fi(r,θ)
      (1)


      where
      D˙l(r,θ) is the absorbed dose rate in liquid water at a given point (r,θ) for a particular applicator i
      K˙50cm is the air kerma rate at a distance of 50 cm, measured in air
      χi(1cm,π/2) is the dose rate conversion coefficient (DRCC) at 1 cm and π/2 for applicator i
      Gp(r,θ) is the geometry function, using the point source approximation?
      gi(r) is the radial dose function for applicator i
      Fi(r,θ) is the 2D anisotropy function for applicator i.
      The three most notable changes in this formalism are the dependence upon the applicator being used, the shift from an air kerma strength standard to air kerma rate measured at 50 cm from the source, and the use of the DRCC, χi(
      • DeWerd LA
      • Culberson WS
      • Micka JA
      • Simiele SJ
      A modified dose calculation formalism for electronic brachytherapy sources.
      ). This value is defined as,
      χi=D˙i(1cm,π/2)K˙50cm.
      (2)


      In order to appropriately characterize these sources, a stable, small volume dosimeter should be used to obtain accurate results. Previous work has used TLD100 microcubes as well as microionization chambers for measurement of these parameters (
      • Rivard MJ
      • Davis SD
      • DeWerd LA
      • et al.
      Calculated and measured brachytherapy dosimetry parameters in water for the Xoft Axxent X-Ray Source: An electronic brachytherapy source.

      TL Pike, A dosimetric characterization of an electronic brachytherapy source in terms of absorbed dose to water, University of Wisconsin- Madison, 2012.

      ). TLD100 microcubes are suitable for this application as they have a small volume of 1 mm3 minimizing volume averaging effects caused in the dosimeter. These dosimeters are passive dosimeters and must be read out following irradiation. This property makes it difficult to adjust any positioning uncertainties observed with the measurements, making this method more time consuming (
      • Kry SF
      • Alvarez P
      • Cygler JE
      • et al.
      AAPM TG 191: clinical use of luminescent dosimeters: TLDs and OSLDs.
      ,
      • Reed JL
      • Rivard MJ
      • Micka JA
      • et al.
      Experimental and Monte Carlo dosimetric characterization of a 1cm 103Pd brachytherapy source.
      ,
      • Da Rosa LAR
      • Regulla DF
      • Fill UA
      Reproducibility study of TLD-100 micro-cubes at radiotherapy dose level.
      • Cameron JR
      • Zimmerman D
      • Kenney G
      • et al.
      Thermoluminescent radiation dosimetry utilizing LiF.
      ). Microionization chambers have a larger volume and may have a variable response. Traditionally, some of these chambers have been known to have a high energy dependence and polarity effects and are unstable over time as observed with calibration data as well as regular quality assurance tests. Additionally, obtaining a stable signal with depth for low energy photon sources can be challenging. The new Exradin A26 ionization chamber is a microionization chamber that has a very small polarity effect and a relatively constant energy dependence, and has been shown to exhibit behavior of a reference class ionization chamber described in TG51 and the subsequent addendum (
      • Miller JR
      • Hooten BD
      • Micka JA
      • DeWerd LA
      Polarity effects and apparent ion recombination in microionization chambers.
      ,
      • Almond PR
      • Biggs PJ
      • Coursey BM
      • et al.
      AAPM's TG-51 protocol for clinical reference dosimetry of high-energy photon and electron beams.
      • McEwen M
      • DeWerd LA
      • Ibbott G
      • et al.
      Addendum to the AAPM's TG-51 protocol for clinical reference dosimetry of high-energy photon beams.
      ). This chamber has a spot size with a diameter of 4.3 mm and collecting volume of 0.015 cc [

      S Imaging, “ION CHAMBERS EXRADIN A26,” vol. i. [Online]. Available: https://static.standardimaging.com/literature/ExradinA26_DS_1363-21.pdf (Accessed July 2021).

      ]. While this volume is larger than the microcubes, the use of this chamber for Xoft Axxent dosimetric measurements was of interest for this work, as it provides instant feedback on the measurement set up (

      S Imaging, “ION CHAMBERS EXRADIN A26,” vol. i. [Online]. Available: https://static.standardimaging.com/literature/ExradinA26_DS_1363-21.pdf (Accessed July 2021).

      ). This active measurement would allow for the user to assess if the source and chamber were misaligned in the vertical direction such that the source was not at a 90° polar angle from the dosimeter. This feedback would allow for the set-up to be adjusted without have to perform a full set of measurements with a new round of TLDs. An additional dosimeter that has been investigated is radiochromic film. While film is also a passive dosimeter it allows for the measurement of a continuous dose distribution rather than measurements at discrete points (
      • Niroomand-Rad A
      • Chiu-Tsao S
      • Grams MP
      • et al.
      Report of AAPM task group 235 Radiochromic film dosimetry: an update to TG-55.
      ,
      • Niroomand-Rad A
      • Blackwell CR
      • Coursey BM
      • et al.
      Radiochromic film dosimetry: Recommendations of AAPM radiation therapy committee task group 55.
      • Schneider F
      • Fuchs H
      • Lorenz F
      • et al.
      A novel device for intravaginal electronic brachytherapy.
      ).
      The overall goal of this work was to measure the radial dose distributions, radial dose function, dose rate conversion coefficient, and polar anisotropy function for the new 7600 Xoft Axxent source using a variety of passive and active dosimeters. The results in this work will assist in the accurate use of these sources in the clinical setting.

      Methods and materials

      TLD100 Microcube measurements

      LiF:Mg,Ti TLD100 microcubes were used to measure both radial dose function and polar anisotropy function. The microcubes have a volume of 1 mm3 and have historically been used for eBt characterization. Prior to measurements, a set of 900 microcubes was annealed for 1 h at 400˚ C, allowed to cool, and then annealed for 24 h at 80˚C (
      • Cameron JR
      • Zimmerman D
      • Kenney G
      • et al.
      Thermoluminescent radiation dosimetry utilizing LiF.
      ). The set of microcubes was irradiated in Cs-137−35 mGy to sort the microcubes by chip factor (CF). The microcubes were left to rest and allow for the traps to settle for 24 h and were then read out using a Harshaw 5500 TLD reader. The CF was calculated by taking the ratio of the response of a given TLD to the median response of the set of TLDs. The set was then annealed for 24 h at 80˚C, and this sorting process was repeated twice more. The standard deviations of the three CFs were calculated, and only microcubes that had less than a 3% variability were used for this work.
      Prior to measurements, the microcubes were irradiated to doses ranging from 50 to 1000 cGy using either a Theratron T1000 or Hopewell G100 Co-60 irradiator. Three TLDs were irradiated at each dose and were used to obtain a calibration curve to calculate dose measured with the microcubes. Additionally, 6 microcubes were set aside to correct for background irradiation. This calibration process was repeated for each round of measurements made for this work.
      The radial dose function measurements were made using the Captain's wheel phantom previously developed at the University of Wisconsin Medical Radiation Research Center (UWMRRC) (

      TL Pike, A dosimetric characterization of an electronic brachytherapy source in terms of absorbed dose to water, University of Wisconsin- Madison, 2012.

      ). This phantom is constructed of Virtual Water (Med Cal, Verona, WI) and features posts that are machined to securely hold the microcubes. The microcubes were secured in place using plastic wrap and a rubber o-ring to ensure they were waterproof. The posts were placed at 30˚ increments around the Axxent source at 11 positions. The remaining position was occupied by an Exradin A16 ionization chamber (Standard Imaging, Middleton, WI) to correct for timing of the source as well as monitor source output over the measurement sequence. The posts and source were aligned using aluminum gauges machined to place the microcubes at radial distances of 1−4 cm from the source, with only one radial distance measured at a time. The posts were pushed up against the gauge and secured in place. The source was then placed in the phantom and into a center hole machined in the gauge, then secured in place. The gauge was removed, and measurements were made using three different sources at each radial distance, and three measurements per distance per source were made.
      Following a 24-h rest period, the microcubes were read out, and dose rate in water was calculated using:
      D˙w=M*N*(kbq)Co60AxxentC(1cm,90)*t,
      (3)


      where M is the light output of the TLD, with the applied CF and corrected for background, N is the calibration coefficient determined from the Co-60 calibration, (kbq)Co60Axxent is an energy correction factor, adopted from the work of Pike (

      TL Pike, A dosimetric characterization of an electronic brachytherapy source in terms of absorbed dose to water, University of Wisconsin- Madison, 2012.

      ), C(1 cm, 90˚) is the phantom correction factor, adopted from the work of Simiele (

      SJ Simiele, Advancements in electronic brachytherapy dosimetry methods, University of Wisconsin-Madison, 2017.

      ), and t is the effective time, determined using the A16 ionization chamber. The radial dose function at a given radial distance, r, was then calculated as,
      g(r)=D˙w(r)D˙w(1cm)Gp(r0,θ0)GP(r,θ0),
      (4)


      where Gp(r0,θ0)GP(r,θ0) accounts for the r2 fall off of the source. As per DeWerd et al. (
      • DeWerd LA
      • Culberson WS
      • Micka JA
      • Simiele SJ
      A modified dose calculation formalism for electronic brachytherapy sources.
      ), the point source approximation is used with the assumption that the x-rays originate from a single point on the anode and is considered the best approximation for these types of sources. The measured dose rates at each distance were also used to determine the relative radial dose distributions.
      The polar anisotropy measurements were made using a PMMA phantom previously developed in-house by Simiele (

      SJ Simiele, Advancements in electronic brachytherapy dosimetry methods, University of Wisconsin-Madison, 2017.

      ). This phantom features acrylic posts that allow for the microcubes to be securely placed around the source at distances of 1, 2, and 5 cm. The phantom was constructed such that the measurements were made from 0˚ to 150˚ at 1 cm, 0˚ to 165˚ at 2 cm, and 0˚ to 172.5˚ at 5 cm. The posts were spaced apart by 30˚, 15˚, 7.5˚ for 1 cm, 2 cm, and 5 cm measurements, respectively. Due to the known azimuthal anisotropy of the source, the phantom was rotated evenly around the vertical axis of the source during the duration of the measurement using a string attached to the phantom and a rotating platform. These measurements were made for 3 sources, and measurements were repeated at least 3 times per source per distance.
      Following the 24-h rest period, the microcubes were read out and corrected following Eq. 3. The microcubes located across from each other were averaged for a given angle. The polar anisotropy was then calculated as,
      F(r,θ)=Mcorr,θMcorr,90Gp(r,θ0)GP(r,θ),
      (5)


      Mcorr indicates the corrected light output.
      The phantom correction factors for the polar anisotropy function were simulated using the track length estimator (TLE) made available in the v3.7 release of TOPAS Monte Carlo user code (
      • Perl J
      • Shin J
      • Schümann J
      • et al.
      TOPAS: An innovative proton Monte Carlo platform for research and clinical applications.
      ,
      • Berumen F
      • Ma Y
      • Ramos-Méndez J
      • et al.
      Validation of the TOPAS Monte Carlo toolkit for HDR brachytherapy simulations.
      ). These factors were simulated by scoring dose to 1 mm3 volumes of water and LiF:MgTi TLD100 material located at the respective polar angles measured with this phantom. An example of this simulation geometry is shown in Fig. 1.
      Fig 1
      Fig. 1The polar anisotropy phantom correction factor simulation geometry, as modelled using the TOPAS Monte Carlo user code.
      The Axxent source was modelled using the G4PolyCone class (
      • Agostinelli S
      • Allison J
      • Amako K
      • et al.
      GEANT4 - A simulation toolkit.
      ) and modelled per manufacturer specifications. A pencil beam electron source was used to simulate the photon production within the source, using the physics parameters outlined in Table 1. The dose to water simulations were used by scoring the doses at 1 cm, 2 cm, and 5 cm radial distances simultaneously. These volumes and the source were placed in a 30 cm × 30 cm × 30 cm water phantom using 5 × 107 starting electron histories. These simulations were then repeated by replacing the water phantom with PMMA and the water volumes with the TLD material. The simulation of the dose to TLD at each radial distance was performed separately for these simulations to replicate the experimental set up, where only one radial distance was considered at a time to match the simulation scatter conditions to experimental scatter conditions. A total of 107 starting electron histories were run for the 1 cm and 2 cm radial distances, while 5 × 107 starting electron histories were used at the 5 cm distance.
      Table 1A list of the physics parameters used to simulate the phantom correction factors for the polar anisotropy function measurements using the TOPAS Monte Carlo user code
      Physics parameterValue
      Variance reduction: uniform bremsstrahlung splitting10,000
      Physics modulesG4em-standard_opt4

      G4em-extra

      G4em-livermore

      G4em-standard_GS
      EmRangeMin50 eV
      AugerTrue
      Auger CascadeFalse
      FluorescenceTrue
      PIXETrue
      Deexcitation Ignore CutsFalse
      Cut For Electron0.5 nm
      Cut For Gamma0.1 nm
      Set Production Cut Lower Edge1 keV

      Gafchromic film measurements

      A PMMA ring phantom was designed in house at the UWMRRC to be used with phantoms from previous works (

      SJ Simiele, Advancements in electronic brachytherapy dosimetry methods, University of Wisconsin-Madison, 2017.

      ). This phantom, shown in Fig. 2, allows for 3 cm wide strips of Gafchromic EBT3 film (Ashland, Inc.) to be cut and wrapped 360˚ around the source. This phantom was designed such that piece of film was tightly placed between the two pieces of acrylic, minimizing any air gaps. The ring phantom was placed in a stack of slabs of PMMA with both a ring insert as well as a slot for the source to sit rigidly. The rings were designed such that the source anode was placed approximately in the center of the film. Measurements were made at radial distances of 1−4 cm from the source anode for three sources, and three films per distance per source were irradiated.
      Fig 2
      Fig. 2The PMMA ring film holder used to irradiate the EBT3 film to measure the radial dose profiles for the S7600 source.
      The films were read out on an EPSON Flatbed scanner. The irradiated films were corrected for any pre-irradiation noise in the film as well as background radiation. Line profiles were drawn through the highest optical density region to obtain relative radial dose distributions.

      A26 ionization chamber measurements

      The Exradin A26 microionization chamber was used in both the Captain's wheel phantom and an acrylic holder designed in-house, shown in Fig. 3 (

      SJ Simiele, Advancements in electronic brachytherapy dosimetry methods, University of Wisconsin-Madison, 2017.

      ,

      TL Pike, A dosimetric characterization of an electronic brachytherapy source in terms of absorbed dose to water, University of Wisconsin- Madison, 2012.

      ). The Captain's wheel measurements were used to assess the relative signal that could be measured with the chamber as well as evaluate the relative radial dose distributions. For these measurements, the chamber tip was aligned with the aluminum gauge, and the source was aligned in the same way as the TLD measurements. The A16 chamber was used to monitor the output of the source over the duration of the measurements, similar to the TLD measurement methods. The A26 chamber was placed in each of the 11 positions around the source at each distance, and three, 30 second charge readings were taken at each position. These measured signals at each position were used to plot the relative dose distributions for the Axxent sources.
      Fig 3
      Fig. 3The S7600 source (center) and A26 chamber (left) placed in the acrylic phantom used to take radial dose measurements in water. Here, the chamber is located at a 2 cm radial distance from the source.
      The acrylic phantom was used for absolute dose measurements using the A26 chamber. This chamber was chosen for absolute dose measurements rather than the A16 chamber due to its increased stability both over time and with depth in water for the measurement of these low energy sources (
      • Miller JR
      • Hooten BD
      • Micka JA
      • DeWerd LA
      Polarity effects and apparent ion recombination in microionization chambers.
      ). The source was placed in the center of the phantom, and the chamber was placed at distances of 1−4 cm from the source. An acrylic block was used prior to irradiation to align the source to the active volume of the chamber. Measurements were made at the four cardinal angles around the source for three different sources. Three, 30 second charge readings were taken at each position, and the dose rate in water was then calculated using,
      D˙w(r)=M*NkM50*PTP*Ppol*Pion*Pelec*DwM50KM50*kvol*(kbq)M50Axxent,
      (6)


      where M is the raw charge reading, NkM50 is the air kerma rate calibration coefficient, measured in the UW M50 beam, PTP corrects for temperature and pressure, Ppol is the polarity correction factor, Pioncorrects for ionic recombination, Pelec is the electrometer calibration factor, DwM50KM50 converts the air-kerma of the M50 beam to absorbed dose to water of the M50 beam and was previously determined at the UWMRRC, kvol accounts for volume averaging effects of the chamber, determined using the EGSnrc user code, and (kbq)M50Axxent is the energy dependence of the chamber to account for dependence between the M50 and Axxent source average energies (

      S Imaging, “ION CHAMBERS EXRADIN A26,” vol. i. [Online]. Available: https://static.standardimaging.com/literature/ExradinA26_DS_1363-21.pdf (Accessed July 2021).

      ,

      MJ Lawless, Development of kilovoltage x-ray dosimetry methods for their applications to cone beam computed tomography, University of Wisconsin Madison, 2016.

      ). While these two beam energies are close in proximity, they fall within the low energy region of the energy dependence curve. This region has a steeper energy dependence and results in a 10% difference in energy responses for the two beam qualities. The average dose rates at each position were then used in Eq. 6 to calculate radial dose function and Eq. 2 to calculate the DRCC. The air kerma rate was determined using Attix free air chamber at the UWMRCC, following the methods outlined in Walter et al. (
      • Walter AE
      • Hull JL
      • DeWerd LA
      Comparison of air kerma rate between the S7500 and S7600 Xoft Axxent sources.
      ).

      Results

      Radial dose distributions

      Figure 4 shows the measured radial dose distributions with the TLD100 microcubes, EBT3 film and the A26 ionization chamber. For all measurements, the results were normalized to the 0˚ position. Note, for the chamber measurements, the A16 chamber was placed at 270° and for the microcube measurements the A16 was placed at 240°.
      Fig 4
      Fig. 4Radial dose distributions measured with (A) EBT3 film, (B) A26 ionization chamber, (C) TLD100 microcubes. The gap observed at 270 and 240 represent the location of the monitor chamber.
      An average standard deviation in the measurements of approximately 4% was observed for the microcube measurements and was not dependent on the radial distance. Standard deviations for the film measurements ranged from 2.2% at 1 cm to 5.5% at 4 cm radial distances. Chamber standard deviations ranged from 0.05% at 1 cm to 0.50% at 4 cm radial distances.

      Radial dose function

      Results for the radial dose function values measured with the microcubes and the A26 chamber are shown in Table 2.
      Table 2Radial dose function values as measured with the TLD100 microcubes and A26 ionization chamber. The uncertainties listed are the expanded uncertainties (k = 2)
      Radial distance (cm)TLD100

      Microcubes (%)
      A26 chamber (%)Percent difference

      11.000 ± 0.174 (17.4%)1.000 ± 0.032 (8.6%)0.0%
      20.682 ± 0.124 (18.3%)0.645 ± 0.021 (8.6%)5.7%
      30.508 ± 0.100 (19.6%)0.475 ± 0.016 (8.7%)6.9%
      40.309 ± 0.167 (54.2%)0.361 ± 0.015 (9.1%)-14%
      The microcube and A26 measurements are the average values obtained from the same three source measurements. Note, the larger standard deviations of the microcube measurements are representative of the systematic shift observed with the measured dose distributions at the 1 cm radial distance.

      Dose rate conversion coefficient

      An uncertainty budget for the TLD measurements at 1 cm for the DRCC are shown in Table 3. The uncertainty in the air kerma measurement used for determining the DRCC is adopted from Walter et al. (
      • Walter AE
      • Hull JL
      • DeWerd LA
      Comparison of air kerma rate between the S7500 and S7600 Xoft Axxent sources.
      ). The uncertainty in the determination of the radial dose function follows a similar format to Table 3.
      Table 3The uncertainty budget for determining the absorbed dose to water at a 1 cm radial distance from the S7600 source using TLD 100 microcubes in the Captain's wheel phantom
      QuantityType A (%)Type B (%)
      TLD reproducibility1.6
      TLD irradiation time0.33
      TLD reader stability0.10
      Measured azimuthal anisotropy7.0
      Source positioning4.5
      Calibration1.35
      Phantom correction factor0.070.00
      Intrinsic energy dependence0.990.97
      Combined uncertainty7.254.81
      Standard total uncertainty (k = 1)8.70
      Expanded uncertainty (k = 2)17.4
      Here, the reproducibility of the TLDs accounts for the average variation in dose rate measured at a given angle. The irradiation time, source positioning, and phantom correction factor components were adopted from the work of Simiele (

      TL Pike, A dosimetric characterization of an electronic brachytherapy source in terms of absorbed dose to water, University of Wisconsin- Madison, 2012.

      ). The TLD reader stability was adopted from the work of Raffi (

      J Raffi, Limitations of current dosimetry for intracavitary partial breast irradiation with high dose rate 192Ir and electornic brachytherapy sources, University of Wisconsin-Madison, 2016.

      ). The azimuthal anisotropy accounts for the standard deviation of the average of the 11 TLD measurements for a given measurement point to account for the azimuthal anisotropy; this was taken as a rectangular distribution and included as a Type A uncertainty as it was adopted from the measured results. The calibration accounts for the standard deviation of both the expected dose delivered from the 60Co irradiator as well as the uncertainty in the air kerma rate. Finally, the intrinsic energy dependence accounts for the experimental and simulation uncertainty in determining the energy dependence of the TLD measurement, adopted from the work of Pike (

      TL Pike, A dosimetric characterization of an electronic brachytherapy source in terms of absorbed dose to water, University of Wisconsin- Madison, 2012.

      ). A similar uncertainty budget can be adapted for the other radial distances measured with the Captain's wheel for the radial dose function measurements.
      The uncertainty budget for the determination of the absorbed dose to water at 1 cm using the A26 chamber for the DRCC is shown in Table 4. The uncertainty in the air kerma measurement used for determining the DRCC is adopted from Walter et al. (
      • Walter AE
      • Hull JL
      • DeWerd LA
      Comparison of air kerma rate between the S7500 and S7600 Xoft Axxent sources.
      ). The uncertainty in the determination of the radial dose function follows a similar format to Table 4.
      Table 4The uncertainty budget for determining the absorbed dose to water at a 1 cm radial distance from the S7600 source using the A26 microionization chamber
      QuantityType A (%)Type B (%)
      Chamber measurements0.20
      Electrometer calibration0.17
      Air density0.10
      Azimuthal anisotropy4.04
      Ion recombination0.05
      Polarity0.05
      Dw to K conversion0.50
      Volume correction0.50
      Energy correction0.50
      Calibration uncertainty0.50
      Combined uncertainty0.051.02
      Standard total uncertainty (k = 1)4.31
      Expanded uncertainty (k = 2)8.62
      Here, the uncertainty in the chamber measurement represents the standard deviation of the repeated measurements of a single source. The azimuthal anisotropy accounts for the variation of the source output as a function of azimuthal angle, approximated as a rectangular distribution using the ±7% variation communication by the manufacturer (

      SJ Simiele, Advancements in electronic brachytherapy dosimetry methods, University of Wisconsin-Madison, 2017.

      ). The recombination, polarity, and energy correction uncertainty are adopted from the chamber specifications from the work of Miller et al. (
      • Miller JR
      • Hooten BD
      • Micka JA
      • DeWerd LA
      Polarity effects and apparent ion recombination in microionization chambers.
      ). The electrometer uncertainty and calibration uncertainty are taken from the calibration reports obtained from the UWADCL. The dose to water to kerma conversion has been pre-determined at the UWMRRC and accounts for the uncertainty in converting the air-kerma calibration to dose to water. Finally, the volume correction factor accounts for the uncertainty in the Monte Carlo simulation used to account for the volume of the chamber.
      The DRCC values measured with the microcubes and A26 chamber were 10.35 ± 0.91 cGy/hrμGy/min and 9.33 ± 0.58 cGy/hrμGy/min, respectively. Note that while a nearly 11% difference between the two values is present, the results do agree within the k = 2 uncertainty in the measurements shown.

      Polar anisotropy

      Figure 5 shows the polar anisotropy plotted as a function of polar angle. The error bars represent the expanded uncertainty (k = 2), and these quantities are included with the measured values listed in Table 4.
      Fig 5
      Fig. 5The TLD-100 microcube measured polar anisotropy functions for radial distances of 1, 2, and 5 cm. The error bars represent the expanded uncertainty (k = 2).
      The uncertainty budget for the measurement of the polar anisotropy function at 1 cm is shown in Table 5. The uncertainties at 2 cm and 5 cm radial distances follow a similar format. The TLD reproducibility in Table 5 accounts for the standard deviation of the dose calculated at a given polar angle, accounting for inter- and intra- source variations. The TLD irradiation time was adapted from the work of Simiele and was estimated from the standard deviation of the A16 timing measurements from the Captain's wheel measurements (

      SJ Simiele, Advancements in electronic brachytherapy dosimetry methods, University of Wisconsin-Madison, 2017.

      ). The TLD reader stability was adapted from the work of Raffi (

      J Raffi, Limitations of current dosimetry for intracavitary partial breast irradiation with high dose rate 192Ir and electornic brachytherapy sources, University of Wisconsin-Madison, 2016.

      ). The source positioning accounts for the placement of the source within the phantom, accounting for whether or not the source is fully flush within the phantom as the phantom rotates during the measurement, taken as a rectangular distribution. The calibration accounts for the standard deviation of both the expected dose delivered from the 60Co irradiator as well as the uncertainty in the air kerma rate. The phantom correction factor accounts for the statistical uncertainty in the TOPAS simulated correction factors. Finally, the intrinsic energy dependence accounts for the experimental and simulation uncertainty in determining the energy dependence of the TLD measurement, adopted from the work of Pike (

      TL Pike, A dosimetric characterization of an electronic brachytherapy source in terms of absorbed dose to water, University of Wisconsin- Madison, 2012.

      ).
      Table 5The uncertainty budget for the determination of the polar anisotropy function using TLD100 microcubes at a 1 cm radial distance. Other radial distances measured follow a similar format
      QuantityType A (%)Type B (%)
      TLD reproducibility3.00
      TLD irradiation time0.33
      TLD reader stability0.10
      Source positioning0.30
      Calibration1.35
      Phantom correction factor2.000.90
      Intrinsic energy dependence0.990.96
      Combined uncertainty3.162.64
      Standard total uncertainty (k = 1)4.22
      Expanded uncertainty (k = 2)8.44

      Discussion

      A systematic shift was observed with the microcube measurements of the radial dose distributions using the Captain's Wheel phantom that was not observed for the film or A26 measurements. This shift can most likely be attributed to uncertainties due to small shifts in the source positioning of the measurement geometry. For example, using a 1/r2 fall off principle, a 1 mm shift can contribute to up to a 20% difference in the dose. The changes made to the source construction made the catheter of the S7600 source more pliable than the S7500 source; thus, these uncertainties were not observed in the works of Pike and Simiele using the same measurement set-up (

      SJ Simiele, Advancements in electronic brachytherapy dosimetry methods, University of Wisconsin-Madison, 2017.

      ,

      TL Pike, A dosimetric characterization of an electronic brachytherapy source in terms of absorbed dose to water, University of Wisconsin- Madison, 2012.

      ). Further, these uncertainties were not observed for the polar anisotropy measurements, as the acrylic phantom allowed for a more rigid source placement with respect to the dosimeters, eliminating the influence of the source flexibility on the measurement.
      Additionally, there may have been machining variations between the posts used for the Captain's wheel measurements, as the same post was used for a given position throughout the measurement sequence. The inconsistencies in the posts could have also contributed to different scatter conditions in the phantom material with respect to the source location. However, this contribution was mostly accounted for in Table 3. This trend was not observed for the A26 measurements using the Captain's wheel and is most likely due to volume averaging effects of the chamber and that the chamber only occupied a single location at a time, minimizing any scatter effects from other detectors in the beam. The film measurements, which were performed in a more rigid set up, are the most symmetric and agree well with the measured chamber results.
      The larger standard deviations observed at 1 cm for the measurement of the polar anisotropy are consistent with the work of Walter et al., where a variation of approximately 7% was observed for the air-kerma rates measured for the S7600 sources (
      • Walter AE
      • Hull JL
      • DeWerd LA
      Comparison of air kerma rate between the S7500 and S7600 Xoft Axxent sources.
      ). Any variations in the manufacturing process can cause differences in the low energy range of the energy spectrum, which can thus influence measurements at shallower distances. Additionally, any uncertainty or variation in the rotation method used for these measurements could influence the measurement at this distance due to shorter irradiation times.
      When comparing the radial dose function values measured with the A26 chamber for the S7600 source to the TLD results from the work of Simiele for the S7500 source, the values at 2 cm, 3 cm, and 4 cm radial distances were 5.6%, 9,9%, and 7.4% greater, respectively (

      SJ Simiele, Advancements in electronic brachytherapy dosimetry methods, University of Wisconsin-Madison, 2017.

      ). The S7600 source penetrates deeper because of beam hardening effects from the new coolant. Thus, the increase in the average energy results in a 5.6% greater penetration at 2 cm. Additionally, the uncertainty observed on the A26 measurements in this work and consistent with those published for the TLD data in Simiele (

      SJ Simiele, Advancements in electronic brachytherapy dosimetry methods, University of Wisconsin-Madison, 2017.

      ). Additionally, previous work measuring the S7500 source indicated this source was more forward directed than the S7600 source. The polar anisotropy function for angles of 0 degrees to 90 degrees for the S7600 source was, on average, 16.5%, 10.3%, and 4.3% lower than the S7500 source for radial distances of 1 cm, 2 cm, and 5 cm, respectively. The largest observed differences were at angles of 0 to 30 degrees for all radial distances and can be attributed to self-filtration caused by an increased thickness of the anode coating as well as attenuation of these filtered photons caused by an increased thickness of Galden at this location. For angles greater than 90 degrees, the average agreement between the values was within the uncertainty of the measurements (

      SJ Simiele, Advancements in electronic brachytherapy dosimetry methods, University of Wisconsin-Madison, 2017.

      ). The variation in the overall polar distributions can be attributed to both the scattering properties of Galden compared to water as well as the increased thickness of titanium tungsten alloy at the anode. Further, the magnitude of the phantom correction factors applied to these measurements was minimal. These results, along with a complete Monte Carlo study, are the focus of future work.
      The variations in dosimetry parameters between the S7500 and S7600 sources can be attributed to both the beam hardening effects of the high-density coolant as well as the change of the anode coating. The filtration of the lower energy, characteristic x-rays caused by the Galden coolant resulted in less energy deposited at shallower depths and can be responsible for the observed differences in radial dose function. Further, the scattering properties of this coolant, paired with the new anode coating, influenced the overall shape of polar anisotropy function compared to the S7500 sources. The increased anode coating thickness also resulted in a reduction of dose rate of the sources which had a minimal influence on these modified TG43 parameters.

      Conclusion

      This work provides values for dosimetric parameters for the bare S7600 Xoft Axxent source. The effects of both the higher density coolant as well as the increase in anode coating thickness influence the dose rate of the sources as well as alter the energy spectrum. These changes result in up to a 10.4% difference in dosimetry parameters and highlights the importance of using source specific parameters. To utilize these sources clinically, work should be performed to determine appropriate, applicator specific, dosimetry parameters.

      Acknowledgments

      The authors would like to thank Tom Rusch, Linda Kelley, Rob Burnside, and Rob Neimeyer from Xoft for their assistance over the duration of this work. They would also like to thank Benjamin Palmer and John Micka for providing assistance with the dosimetric measurements performed in this work. Finally, they would like to thank Samantha Simiele for her guidance throughout the duration of this project.

      Appendix B. Supplementary materials

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