PROFICIENCY TEST OF THE SSDL-ININ-MEXICO FOR THE CALIBRATION OF WELL-TYPE CHAMBERS WITH HDR 192IR SOURCES USING TWO DIFFERENT DOSIMETRY CODES OF PRACTICE FOR THE DETERMINATION OF REFERENCE AIR KERMA RATE K ̇ R

PROFICIENCY TEST OF THE SSDL-ININ-MEXICO FOR THE CALIBRATION OF WELL-TYPE CHAMBERS WITH HDR 192IR... Abstract The results of the comparison between SSDL-ININ and SSDL-CPHR (pilot laboratory) demonstrates the competence of the SSDL-ININ for the performance of the K̇R in 192Ir. The RININ/CHPR ratio for the calibration coefficients is 0.989 ± 0.005. The comparison uses three SI-HDR 1000-Plus as transfer chambers, series: A02423, A941755 and A973052. CPHR used a secondary standard PTW 3304 chamber, s/n 154, calibrated at PTB and ININ employed a secondary standard SI-90008 s/n A963391, calibrated at NPL. To determine K̇R, the SSDL-CPHR used the IAEA TEC-DOC-1274 and the SSDL-ININ used the IPEM (UK) code of practice. The latter uses a correction factor by source’s geometry, ksg. The results show that both codes are equivalent; however, for the use of well chambers in the highlands or in locations with reduced atmospheric pressure, it is needed to apply an additional factor k′P, or, to design a well chamber with air-equivalent walls for the application of the conventional kPT. INTRODUCTION In Latin America, uterine cervical cancer is the second cause of death among women(1). This neoplasm is usually treated with surgery and/or high and low dose rate brachytherapy (BT), with 192Ir sources and sets of 137Cs sources, respectively(2). However, to achieve success in tumor control using external beam radiotherapy (RT) and/or BT, the restrictions on accuracy and precision are that the absorbed dose given to the tumoral volume has an expanded uncertainty U(k=2)<5% for RT and U(k=2)<10% for BT(3). To guarantee the fullfilment of these and other quality control constrictions, the IAEA/WHO SSDL network of dosimetry laboratories provide calibration services and dosimetry support to the RT centers in each country, where them are located(4). Requirements of the ISO 17025 for comparisons On the other hand, a general requirement of the ISO 17025 is that calibration laboratories demonstrate their technical competence through comparisons between laboratories and/or proficiency tests(5). For the primary laboratories of the National Institutes of Metrology and Institutes designated under the CIPM Mutual Recognition Agreement(6), these comparisons, in the case of high dose rate BT, correspond to the key comparison BIPM RI(I)-K8, for rate of reference air kerma ( KṘ) with 192Ir sources(7). In the case of SSDL’s, however, these comparisons are usually bilateral comparisons, where the pilot laboratory is a primary laboratory(8–10). There are also bilateral comparisons between SSDL’s such as the one conducted between ADCL of the U. Wisconsin and the Laboratory of Radiological Sciences of the Catholic University of Rio de Janeiro, Brazil; where the calibration of the source is performed using the 7-point method, and a well chamber is used as the transfer chamber(11). However, an underlying problem in these comparisons is that the secondary standard is calibrated with a source type 192Ir at the primary laboratory with a primary standard chamber, and the Hospital or the SSDL use other similar type of source, but with different geometry, design and construction (Table 1)(9, 10). Table 1. Characteristics of the 192Ir sources used in bilateral comparison ININ-CPHR. Source type Active core Encapsulation Location Isotope Length (mm) Diameter (mm) Stain steel Thickness (mm) Outer diameter (mm) Length (mm) Microselectron V2 192Ir 3.60 0.65 AISI316 0.125 0.90 4.50 PTB, Braunschweig, DECancer Center, Hospital ABC, Mexico City, MX Isodose control Flexisource 192Ir 3.50 0.60 AISI316L 0.20 0.86 4.60 NPL, Teddington, UK Source type Active core Encapsulation Location Isotope Length (mm) Diameter (mm) Stain steel Thickness (mm) Outer diameter (mm) Length (mm) Microselectron V2 192Ir 3.60 0.65 AISI316 0.125 0.90 4.50 PTB, Braunschweig, DECancer Center, Hospital ABC, Mexico City, MX Isodose control Flexisource 192Ir 3.50 0.60 AISI316L 0.20 0.86 4.60 NPL, Teddington, UK Table 1. Characteristics of the 192Ir sources used in bilateral comparison ININ-CPHR. Source type Active core Encapsulation Location Isotope Length (mm) Diameter (mm) Stain steel Thickness (mm) Outer diameter (mm) Length (mm) Microselectron V2 192Ir 3.60 0.65 AISI316 0.125 0.90 4.50 PTB, Braunschweig, DECancer Center, Hospital ABC, Mexico City, MX Isodose control Flexisource 192Ir 3.50 0.60 AISI316L 0.20 0.86 4.60 NPL, Teddington, UK Source type Active core Encapsulation Location Isotope Length (mm) Diameter (mm) Stain steel Thickness (mm) Outer diameter (mm) Length (mm) Microselectron V2 192Ir 3.60 0.65 AISI316 0.125 0.90 4.50 PTB, Braunschweig, DECancer Center, Hospital ABC, Mexico City, MX Isodose control Flexisource 192Ir 3.50 0.60 AISI316L 0.20 0.86 4.60 NPL, Teddington, UK Proposed solution on the use of different sources for the calibration process at a SSDL and/or hospital This problem is solved by: The use at the SSDL or hospital of a calibration source equal to the one used at the primary laboratory. By means of a dosimetry code of practice for K̇R that considers a correction factor for the geometric differences of the calibration sources ksg(12). Additionally, there is another approximation that introduces a component of uncertainty that considers the variation of the source types(10, 11, 13); however, this does not solve the problem. Therefore, the aim of this work is to demonstrate the technical competence of the SSDL-ININ-México for its calibration and measurement capability (CMC) in the K̇R quantity for 192Ir sources, for the calibration of well chambers, (with the use of the dosimetry code of practice developed by the IPEM that considers a source geometry correction factor(12)), by a bilateral comparison with the SSDL-CPHR-Cuba. (Which in turn employs the IAEA calibration codes of practice TEC 1274, and adding an uncertainty component by using different design sources on the calibration process(14).) In particular, the SSDL-CPHR-Cuba is the pilot laboratory given its experience in bilateral comparisons(9, 10); this SSDL uses the secondary standard PTW model 33004 serial 0154 (with a nominal volume 116 cm3), calibrated at the PTB in 2013. The secondary standard of the SSDL-ININ is a Standard Imaging model HDR-100 Plus s/n A963391 (with a nominal volume 245 cm3) calibrated at the NPL in the year 2016; both chambers are calibrated in terms of KR, see Tables 1 and 4 for a detailed description of the sources, chambers and holders used. The comparison is performed at the Radiotherapy Department on the Cancer Center of the Hospital ABC, located in Mexico City, which has a MicroSelectron source V2 (Table 1). The laboratories have agreed to evaluate the results obtained using the normalized error value, En, as recommended in ISO/IEC 17043(15). In the next section, the dosimetry codes of practice employed on the calibration of radioactive sources and the well chamber are discussed. DOSIMETRY CODES OF PRACTICE FOR THE CALIBRATION OF WELL CHAMBERS IN TERMS OF K̇R There are two basic techniques for the calibration of high and low dose rate BT sources in terms of K̇R, which are briefly described below(14). The reader can find more details in the review article(16). Determination of K̇R with a cavity ionization chamber at the reference distance The basic formula for determining K̇R from the air kerma rate is given by the following equation(14): K̇R=NK̇R⋅(Q/t)⋅kel⋅kP,T⋅kpol⋅krec⋅kscat⋅katt⋅kn⋅[ddr]2 (1) where K̇R, is the reference kerma rate [Gy s−1] defined in references(17, 18). NK̇R is the calibration factor for a standard chamber calibrated in air kerma for 192Ir [Gy/C](11–14, 16, 19, 20). Q, integrated charge [C]. t, integration time [s]. kel, kP,T, kpol, krec, kscat, katt, kn, d and dr are the calibration factor of the electrometer; corrections for atmospheric pressure and temperature; polarization; recombination losses; scattering; attenuation; a non-uniformity correction factor that accounts for the non-uniform electron fluence within the air cavity, the distance between the center of the source and the center of the ionization chamber; and the reference distance of 1 m, respectively. Determination of K̇R with a well chamber There are two basic codes of practice for determining the K̇R using a well chamber: The general code of practice without correction for the difference between the geometry of the calibration source in relation to the source to be calibrated(14). K̇R=NK̇R⋅(Q/t)⋅kel⋅kP,T⋅krec⋅kdec (2a) Here, K̇R is the air kerma reference rate; NKR is the calibration factor of the well chamber (determined with a calibrated source); Q is the charge measurement [C]; T is the integration time [s]. The code of practice where the correction factor for differences in the geometry of the calibration source and the source to be calibrated ksg(12), in Eq. (2b) is applied: K̇R=NK̇R⋅(Q/t)⋅kel⋅kP,T⋅krec⋅kdec⋅ksg, (2b) here, each component was defined in Eqs. (1) and (2a). Calibration of a well chamber in terms of K̇R The expression for the calibration of a well chamber is as follows(14): NK̇R=K̇R(Q/t)⋅kel⋅kPT⋅krec⋅kdec, (3) where, each term has already been defined previously. Once the calibration coefficients for each laboratory are determined from (3), the competence of the SSDL-ININ is evaluated according to the ISO/IEC 17043 Conformity assessment—General requirements for proficiency testing(15), the normalized error En is one of the statistics proposed for evaluating the performance of a comparison, in particular: En=NK,ININ−NK,CPHRUK,ININ2+UK,CPHR2 (4) where NK,ININ is the calibration coefficient reported by ININ. NK,CPHR is the calibration coefficient reported by CHPR. UK,ININ(k=2) is the expanded standard uncertainty reported by the ININ, for a 95% confidence interval. UK,CHPR(k=2) is the expanded standard uncertainty reported by the CPHR, for a 95% confidence interval. This statistic normalizes the difference of values of the calibration coefficients reported by both laboratories with respect to their associated expanded uncertainties. Experimental conditions and procedure for the bilateral comparison The comparison exercise considers two parts: A set of specific experimental conditions for the standard and transfer chambers. A procedure for realizing the comparison. Experimental conditions for the comparison Table 2 summarizes the standard and transfer well chambers used during the comparison. An important condition is that each chamber has its own (one or several) source holders. The calibration factor refers to the integral instrument, i.e. chamber plus holder. For the determination of the K̇R using the secondary standard instrument, the holder used at the Primary Standard Dosimetry Laboratory during calibration was applied. In a similar way, for the calibration of the transfer chamber, its own source holder was used. Since, a change of holder than the one used in the well chamber calibration at the primary or secondary laboratory implies a change in its calibration factor(21). Table 2. The standards and transfer well chambers used in the bilateral comparison ININ-CPHR. SSDLa Hierarchy/traceability Brand Model Serial HV/Collected charge sign Holder Hmax/mm Catheter length/mm Step/mm Electrometer/Traceability CPHR Secondary Standard/PTB PTW 33004 00154 +400/ Positive H0379 T33002.1.009 40/ 1382 2.5 Keithley 6517B, s/n 1287710 CENAM Transfer SIa HDR 1000 Plus (90008) A973052 +300/ Negative 70010 A973052 47.5/ 1275 2.5 SI, MAX 4000, s/n F092884 CENAM ININ Secondary Standard/NPL SI HDR 1000 Plus (90008) A963391 +300/ Negative 70010 A963391 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM Transfer SI HDR 1000 Plus (90008) A941755 +300/ Negative 70010 A941755 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM SSDLa Hierarchy/traceability Brand Model Serial HV/Collected charge sign Holder Hmax/mm Catheter length/mm Step/mm Electrometer/Traceability CPHR Secondary Standard/PTB PTW 33004 00154 +400/ Positive H0379 T33002.1.009 40/ 1382 2.5 Keithley 6517B, s/n 1287710 CENAM Transfer SIa HDR 1000 Plus (90008) A973052 +300/ Negative 70010 A973052 47.5/ 1275 2.5 SI, MAX 4000, s/n F092884 CENAM ININ Secondary Standard/NPL SI HDR 1000 Plus (90008) A963391 +300/ Negative 70010 A963391 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM Transfer SI HDR 1000 Plus (90008) A941755 +300/ Negative 70010 A941755 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM aStandard imaging. Table 2. The standards and transfer well chambers used in the bilateral comparison ININ-CPHR. SSDLa Hierarchy/traceability Brand Model Serial HV/Collected charge sign Holder Hmax/mm Catheter length/mm Step/mm Electrometer/Traceability CPHR Secondary Standard/PTB PTW 33004 00154 +400/ Positive H0379 T33002.1.009 40/ 1382 2.5 Keithley 6517B, s/n 1287710 CENAM Transfer SIa HDR 1000 Plus (90008) A973052 +300/ Negative 70010 A973052 47.5/ 1275 2.5 SI, MAX 4000, s/n F092884 CENAM ININ Secondary Standard/NPL SI HDR 1000 Plus (90008) A963391 +300/ Negative 70010 A963391 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM Transfer SI HDR 1000 Plus (90008) A941755 +300/ Negative 70010 A941755 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM SSDLa Hierarchy/traceability Brand Model Serial HV/Collected charge sign Holder Hmax/mm Catheter length/mm Step/mm Electrometer/Traceability CPHR Secondary Standard/PTB PTW 33004 00154 +400/ Positive H0379 T33002.1.009 40/ 1382 2.5 Keithley 6517B, s/n 1287710 CENAM Transfer SIa HDR 1000 Plus (90008) A973052 +300/ Negative 70010 A973052 47.5/ 1275 2.5 SI, MAX 4000, s/n F092884 CENAM ININ Secondary Standard/NPL SI HDR 1000 Plus (90008) A963391 +300/ Negative 70010 A963391 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM Transfer SI HDR 1000 Plus (90008) A941755 +300/ Negative 70010 A941755 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM aStandard imaging. Measurement protocol for the comparison It consists of two stages, namely: Determination of K̇R with the secondary standard chambers. This has seven steps, which are: Measurements of stability of the secondary standard chambers before comparison. Leakage current measurements for said chambers. Determination of the point of maximum response (sweet spot). Five charge measurements for an integration time of 60 s for the SI (Standard Imaging) chambers and 10 measurements with an integration time of 30 s for the PTW chamber, with nominal operating voltage (100%). Five charge measurements for an integration time of 60 s for SI chambers and 10 measurements with an integration time of 30 s for PTW chamber, with operating voltage of 50%, to determine krec. Five charge measurements for an integration time of 60 s for SI chambers and 10 measurements with an integration time of 30 s for the PTW chamber, with operating voltage of −100%, to determine kpol. Stability measurements of the secondary standard chambers after comparison. Calibration of the SI transfer chamber, which consists of six steps, similar to the previous ones except for the polarization correction, see Eq. (3). As mentioned, the comparison took place at the Cancer Center of the Hospital ABC located in Mexico City; a MicroSelectron V2 source was used (Table 1). The atmospheric conditions during the comparison were: Temperature on the chamber cavity 20 ± 1°C measured with a Fluke thermometer model 1521 s/n A68868 with a Hart scientific thermistor, model 5611T serial A881420; calibrated at CENAM (Mexico). Atmospheric pressure: from 773.7 to 775.4 hPa, measured with a Vaisala digital barometer, model PTB 330 serial F2910009, calibrated at CENAM. The relative humidity during the comparison is maintained at 50%. RESULTS AND DISCUSSION Values of the calibration coefficients, expanded uncertainties and associated statistics Table 3 shows the values for K̇R calculated with Eq. (2a) by the CPHR and with Eq. (2b) for the ININ, the calibration coefficient NK̇R is determined by Eq. (3), Δ% is the difference percentage between the values of NK̇R with respect to the CHPR’s value; where the quotient RININ/CPHR is defined as follows: RININ/CPHR=NKRININNKRCPHR=K̇R,ININIININ⋅ICPHRK̇R,CPHR, (5) Table 3. Summary of the results of the bilateral comparison ININ CPHR for K̇R to 192Ir. Well chamber NK̇R 105/Gy A−1 h−1 ± U% (k = 2) K̇R/mGy h−1 ± U% (k = 2)a Δ% RININ/CPHR±uc En ININ CPHR ININ (NPL) CPHR (PTB) A002423 4.645 ± 1.25% 4.701 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.19 0.988 ± 0.008 0.440 A941755 5.041 ± 1.25% 5.099 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.14 0.989 ± 0.009 0.393 A973052 4.627 ± 1.25% 4.679 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.11 0.989 ± 0.008 0.384 Well chamber NK̇R 105/Gy A−1 h−1 ± U% (k = 2) K̇R/mGy h−1 ± U% (k = 2)a Δ% RININ/CPHR±uc En ININ CPHR ININ (NPL) CPHR (PTB) A002423 4.645 ± 1.25% 4.701 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.19 0.988 ± 0.008 0.440 A941755 5.041 ± 1.25% 5.099 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.14 0.989 ± 0.009 0.393 A973052 4.627 ± 1.25% 4.679 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.11 0.989 ± 0.008 0.384 aThe K̇R for source of Microselectron V2 is normalized to 2016 08 22, 18:53 central time of Mexico. Table 3. Summary of the results of the bilateral comparison ININ CPHR for K̇R to 192Ir. Well chamber NK̇R 105/Gy A−1 h−1 ± U% (k = 2) K̇R/mGy h−1 ± U% (k = 2)a Δ% RININ/CPHR±uc En ININ CPHR ININ (NPL) CPHR (PTB) A002423 4.645 ± 1.25% 4.701 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.19 0.988 ± 0.008 0.440 A941755 5.041 ± 1.25% 5.099 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.14 0.989 ± 0.009 0.393 A973052 4.627 ± 1.25% 4.679 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.11 0.989 ± 0.008 0.384 Well chamber NK̇R 105/Gy A−1 h−1 ± U% (k = 2) K̇R/mGy h−1 ± U% (k = 2)a Δ% RININ/CPHR±uc En ININ CPHR ININ (NPL) CPHR (PTB) A002423 4.645 ± 1.25% 4.701 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.19 0.988 ± 0.008 0.440 A941755 5.041 ± 1.25% 5.099 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.14 0.989 ± 0.009 0.393 A973052 4.627 ± 1.25% 4.679 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.11 0.989 ± 0.008 0.384 aThe K̇R for source of Microselectron V2 is normalized to 2016 08 22, 18:53 central time of Mexico. Finally, En is calculated with Eq. (4). The leakage currents measured during the comparison, along with the long and short-term stability reported by each laboratory are summarized in Table 4. Table 4. Summary of leakage currents and short and long-term stability of the standard and transfer well chambers participating on the bilateral comparison CHPR and ININ. SSDL Well chamber/hierarchy Ileak/A Stability % Reference Short term Long term CPHR PTW 00154 Secondary 2.9E−14 0.024 0.29 (9) SI A973052 Transfer −7.3E−14 0.004 0.14 (9) ININ SI A963391 Secondary 22E−14 0.013 0.17 CC IMR RS SI A002423 Transfer −5.6E−14 0.013 0.17 CC IMR RS SI A941755 Transfer −7.2E−14 0.013 0.13 CC IMR RS SSDL Well chamber/hierarchy Ileak/A Stability % Reference Short term Long term CPHR PTW 00154 Secondary 2.9E−14 0.024 0.29 (9) SI A973052 Transfer −7.3E−14 0.004 0.14 (9) ININ SI A963391 Secondary 22E−14 0.013 0.17 CC IMR RS SI A002423 Transfer −5.6E−14 0.013 0.17 CC IMR RS SI A941755 Transfer −7.2E−14 0.013 0.13 CC IMR RS Table 4. Summary of leakage currents and short and long-term stability of the standard and transfer well chambers participating on the bilateral comparison CHPR and ININ. SSDL Well chamber/hierarchy Ileak/A Stability % Reference Short term Long term CPHR PTW 00154 Secondary 2.9E−14 0.024 0.29 (9) SI A973052 Transfer −7.3E−14 0.004 0.14 (9) ININ SI A963391 Secondary 22E−14 0.013 0.17 CC IMR RS SI A002423 Transfer −5.6E−14 0.013 0.17 CC IMR RS SI A941755 Transfer −7.2E−14 0.013 0.13 CC IMR RS SSDL Well chamber/hierarchy Ileak/A Stability % Reference Short term Long term CPHR PTW 00154 Secondary 2.9E−14 0.024 0.29 (9) SI A973052 Transfer −7.3E−14 0.004 0.14 (9) ININ SI A963391 Secondary 22E−14 0.013 0.17 CC IMR RS SI A002423 Transfer −5.6E−14 0.013 0.17 CC IMR RS SI A941755 Transfer −7.2E−14 0.013 0.13 CC IMR RS In Table 4 and Figure 1, CC I-MR-R/S refers to the I-MR R/S control charts(22) for the SI secondary chamber HDR100 Plus s/n A963391, corresponding to 29 determinations of K̇R performed from March 2011 to December 2016 for the Amersham CDCSM 137Cs source, serial EB811. Figure 1. View largeDownload slide I-MR-R/S Control chart for K̇R measurements made with SI A963391 transfer well chamber and the Amersham CDCSM4 137Cs source serial EB811, where MR gives the long-term stability(22). Figure 1. View largeDownload slide I-MR-R/S Control chart for K̇R measurements made with SI A963391 transfer well chamber and the Amersham CDCSM4 137Cs source serial EB811, where MR gives the long-term stability(22). On the other hand, the uncertainty budget for the combined uc and expanded U uncertainties reported in Table 3, are detailed in Tables 5–7; where such uncertainties are calculated with the BIPM-ISO Guide(23). Table 5a. Uncertainty budget for the calibration of the Microselectron V2 source in terms of K̇R using the secondary standard well chamber PTW 3304 serial 0154, measurements made by the SSDL-CPHR at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 9.16E+05 Gy/(A.h) — 1.25 Certificate PTB 6.22–29/13K Long-term stability kest 1.00 1 0.29 — Table 4 Average charge measurement with the standard Q̅std 613.47 ‘nC’a 0.024 — n = 10 Average leak charge Q̅l,std 1.21E−03 ‘nC’a 0.0001 — Integration time 30 s Integration time t 30 s — 0.001 Electrometer calibration factor kel 1.000074 nC/‘nC’a — 0.0005 Keithley 6517B, s/n 1287710 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3059 1 0.01 0.05 P = 773.94 ± 0.06 hPa, T = 19.250 ± 0.006°C Correction factor for polarity effects kpol 1.0026 1 0.04 — V1 = +400 V, V2 = −400 V Correction factor for recombination effects krec 1.0005 1 0.04 — V1/2 = +200 V Correction factor for radioactive decay kdec 1.00002 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0869 1.5656 Reference air kerma rate K̇R 2.454E−02 Gy h−1 Combined uncertainty uc 3.15E−04 G h−1 1.29% Expanded uncertainty U(k=2) 6.30E−04 Gy h−1 2.58% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 9.16E+05 Gy/(A.h) — 1.25 Certificate PTB 6.22–29/13K Long-term stability kest 1.00 1 0.29 — Table 4 Average charge measurement with the standard Q̅std 613.47 ‘nC’a 0.024 — n = 10 Average leak charge Q̅l,std 1.21E−03 ‘nC’a 0.0001 — Integration time 30 s Integration time t 30 s — 0.001 Electrometer calibration factor kel 1.000074 nC/‘nC’a — 0.0005 Keithley 6517B, s/n 1287710 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3059 1 0.01 0.05 P = 773.94 ± 0.06 hPa, T = 19.250 ± 0.006°C Correction factor for polarity effects kpol 1.0026 1 0.04 — V1 = +400 V, V2 = −400 V Correction factor for recombination effects krec 1.0005 1 0.04 — V1/2 = +200 V Correction factor for radioactive decay kdec 1.00002 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0869 1.5656 Reference air kerma rate K̇R 2.454E−02 Gy h−1 Combined uncertainty uc 3.15E−04 G h−1 1.29% Expanded uncertainty U(k=2) 6.30E−04 Gy h−1 2.58% a‘nC’, nominal nC. Table 5a. Uncertainty budget for the calibration of the Microselectron V2 source in terms of K̇R using the secondary standard well chamber PTW 3304 serial 0154, measurements made by the SSDL-CPHR at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 9.16E+05 Gy/(A.h) — 1.25 Certificate PTB 6.22–29/13K Long-term stability kest 1.00 1 0.29 — Table 4 Average charge measurement with the standard Q̅std 613.47 ‘nC’a 0.024 — n = 10 Average leak charge Q̅l,std 1.21E−03 ‘nC’a 0.0001 — Integration time 30 s Integration time t 30 s — 0.001 Electrometer calibration factor kel 1.000074 nC/‘nC’a — 0.0005 Keithley 6517B, s/n 1287710 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3059 1 0.01 0.05 P = 773.94 ± 0.06 hPa, T = 19.250 ± 0.006°C Correction factor for polarity effects kpol 1.0026 1 0.04 — V1 = +400 V, V2 = −400 V Correction factor for recombination effects krec 1.0005 1 0.04 — V1/2 = +200 V Correction factor for radioactive decay kdec 1.00002 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0869 1.5656 Reference air kerma rate K̇R 2.454E−02 Gy h−1 Combined uncertainty uc 3.15E−04 G h−1 1.29% Expanded uncertainty U(k=2) 6.30E−04 Gy h−1 2.58% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 9.16E+05 Gy/(A.h) — 1.25 Certificate PTB 6.22–29/13K Long-term stability kest 1.00 1 0.29 — Table 4 Average charge measurement with the standard Q̅std 613.47 ‘nC’a 0.024 — n = 10 Average leak charge Q̅l,std 1.21E−03 ‘nC’a 0.0001 — Integration time 30 s Integration time t 30 s — 0.001 Electrometer calibration factor kel 1.000074 nC/‘nC’a — 0.0005 Keithley 6517B, s/n 1287710 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3059 1 0.01 0.05 P = 773.94 ± 0.06 hPa, T = 19.250 ± 0.006°C Correction factor for polarity effects kpol 1.0026 1 0.04 — V1 = +400 V, V2 = −400 V Correction factor for recombination effects krec 1.0005 1 0.04 — V1/2 = +200 V Correction factor for radioactive decay kdec 1.00002 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0869 1.5656 Reference air kerma rate K̇R 2.454E−02 Gy h−1 Combined uncertainty uc 3.15E−04 G h−1 1.29% Expanded uncertainty U(k=2) 6.30E−04 Gy h−1 2.58% a‘nC’, nominal nC. Table 5b. Uncertainty budget for the calibration coefficient NK̇R of SI A941755 transfer chamber in terms of K̇R using the Microselectron V2, measurements realized by the SSDL-CPHR at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.454E−02 Gy h−1 — 1.29 Table 5a Long-term stability kest 1.00 1 — 0.15 Table 4 Average charge measurement with the transfer chamber Q̅std −2211.9 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −3.33E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3049 1 0.004 0.05 P = 774.66 ± 0.03 hPa, T = 19.312 ± 0.001°C Correction factor for recombination effects krec 1.0007 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kdec 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 1.6632 Calibration coefficient NKR 5.099E+05 Gy A−1 h−1 Combined uncertainty uc 6.620E+03 Gy A−1 h−1 1.30% Expanded uncertainty U(k=2) 1.324E+04 Gy A−1 h−1 2.60% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.454E−02 Gy h−1 — 1.29 Table 5a Long-term stability kest 1.00 1 — 0.15 Table 4 Average charge measurement with the transfer chamber Q̅std −2211.9 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −3.33E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3049 1 0.004 0.05 P = 774.66 ± 0.03 hPa, T = 19.312 ± 0.001°C Correction factor for recombination effects krec 1.0007 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kdec 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 1.6632 Calibration coefficient NKR 5.099E+05 Gy A−1 h−1 Combined uncertainty uc 6.620E+03 Gy A−1 h−1 1.30% Expanded uncertainty U(k=2) 1.324E+04 Gy A−1 h−1 2.60% a‘nC’, nominal nC. Table 5b. Uncertainty budget for the calibration coefficient NK̇R of SI A941755 transfer chamber in terms of K̇R using the Microselectron V2, measurements realized by the SSDL-CPHR at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.454E−02 Gy h−1 — 1.29 Table 5a Long-term stability kest 1.00 1 — 0.15 Table 4 Average charge measurement with the transfer chamber Q̅std −2211.9 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −3.33E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3049 1 0.004 0.05 P = 774.66 ± 0.03 hPa, T = 19.312 ± 0.001°C Correction factor for recombination effects krec 1.0007 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kdec 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 1.6632 Calibration coefficient NKR 5.099E+05 Gy A−1 h−1 Combined uncertainty uc 6.620E+03 Gy A−1 h−1 1.30% Expanded uncertainty U(k=2) 1.324E+04 Gy A−1 h−1 2.60% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.454E−02 Gy h−1 — 1.29 Table 5a Long-term stability kest 1.00 1 — 0.15 Table 4 Average charge measurement with the transfer chamber Q̅std −2211.9 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −3.33E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3049 1 0.004 0.05 P = 774.66 ± 0.03 hPa, T = 19.312 ± 0.001°C Correction factor for recombination effects krec 1.0007 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kdec 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 1.6632 Calibration coefficient NKR 5.099E+05 Gy A−1 h−1 Combined uncertainty uc 6.620E+03 Gy A−1 h−1 1.30% Expanded uncertainty U(k=2) 1.324E+04 Gy A−1 h−1 2.60% a‘nC’, nominal nC. Table 6a. Uncertainty budget for the calibration of the Microselectron V2 source in terms of K̇R using the secondary standard SI 90008 well chamber serial A963391, measurements realized by the SSDL-ININ at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 127.7 Gy C-1 — 0.4 Certificate NPL 2016030013-1 Long-term stability kest 1.00 1 0.17 — Table 4 Average charge measurement with the standard Q̅std −2418.86 ‘nC’a 0.004 — n = 10 Average leak charge Q̅l,std −3.00E−02 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.0002 1 ms Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.05 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for source’s geometry ksg 1.004 1 — 04 Certificate NPL 2016030013-1 Correction factor for air density kP,T 1.3035 1 0.003 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for polarity effects kpol 0.9999 1 0.0054 — V1 = +300 V, V2 = −300 V Correction factor for recombination effects krec 1.0003 1 0.006 — V1/2 = +150 V Correction factor for radioactive decay kd 1.0010 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.02899 0.3294 Reference air kerma rate K̇R 2.426E−02 Gy h−1 Combined uncertainty uc 1.46E−04 G h−1 0.6% Expanded uncertainty U(k=2) 2.91E−04 Gy h−1 1.2% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 127.7 Gy C-1 — 0.4 Certificate NPL 2016030013-1 Long-term stability kest 1.00 1 0.17 — Table 4 Average charge measurement with the standard Q̅std −2418.86 ‘nC’a 0.004 — n = 10 Average leak charge Q̅l,std −3.00E−02 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.0002 1 ms Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.05 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for source’s geometry ksg 1.004 1 — 04 Certificate NPL 2016030013-1 Correction factor for air density kP,T 1.3035 1 0.003 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for polarity effects kpol 0.9999 1 0.0054 — V1 = +300 V, V2 = −300 V Correction factor for recombination effects krec 1.0003 1 0.006 — V1/2 = +150 V Correction factor for radioactive decay kd 1.0010 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.02899 0.3294 Reference air kerma rate K̇R 2.426E−02 Gy h−1 Combined uncertainty uc 1.46E−04 G h−1 0.6% Expanded uncertainty U(k=2) 2.91E−04 Gy h−1 1.2% a‘nC’, nominal nC. Table 6a. Uncertainty budget for the calibration of the Microselectron V2 source in terms of K̇R using the secondary standard SI 90008 well chamber serial A963391, measurements realized by the SSDL-ININ at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 127.7 Gy C-1 — 0.4 Certificate NPL 2016030013-1 Long-term stability kest 1.00 1 0.17 — Table 4 Average charge measurement with the standard Q̅std −2418.86 ‘nC’a 0.004 — n = 10 Average leak charge Q̅l,std −3.00E−02 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.0002 1 ms Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.05 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for source’s geometry ksg 1.004 1 — 04 Certificate NPL 2016030013-1 Correction factor for air density kP,T 1.3035 1 0.003 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for polarity effects kpol 0.9999 1 0.0054 — V1 = +300 V, V2 = −300 V Correction factor for recombination effects krec 1.0003 1 0.006 — V1/2 = +150 V Correction factor for radioactive decay kd 1.0010 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.02899 0.3294 Reference air kerma rate K̇R 2.426E−02 Gy h−1 Combined uncertainty uc 1.46E−04 G h−1 0.6% Expanded uncertainty U(k=2) 2.91E−04 Gy h−1 1.2% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 127.7 Gy C-1 — 0.4 Certificate NPL 2016030013-1 Long-term stability kest 1.00 1 0.17 — Table 4 Average charge measurement with the standard Q̅std −2418.86 ‘nC’a 0.004 — n = 10 Average leak charge Q̅l,std −3.00E−02 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.0002 1 ms Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.05 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for source’s geometry ksg 1.004 1 — 04 Certificate NPL 2016030013-1 Correction factor for air density kP,T 1.3035 1 0.003 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for polarity effects kpol 0.9999 1 0.0054 — V1 = +300 V, V2 = −300 V Correction factor for recombination effects krec 1.0003 1 0.006 — V1/2 = +150 V Correction factor for radioactive decay kd 1.0010 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.02899 0.3294 Reference air kerma rate K̇R 2.426E−02 Gy h−1 Combined uncertainty uc 1.46E−04 G h−1 0.6% Expanded uncertainty U(k=2) 2.91E−04 Gy h−1 1.2% a‘nC’, nominal nC. Table 6b. Uncertainty budget for the calibration coefficient NK̇R for SI A973052 transfer chamber in terms of K̇R using the Microselectron V2 source, measurements made by the SSDL-ININ at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.426E−02 Gy h−1 — 0.6 Table 6a Long-term stability kest 1.00 1 0.15 — Table 4 Average charge measurement with the transfer chamber Q̅std −2410.2 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −4.35E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibración factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3058 1 0.001 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for recombination effects krec 1.0005 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kd 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 0.3690 Calibration coefficient NKR 4.627E+05 Gy A−1 h−1 Combined uncertainty uc 2.92E+03 Gy A−1 h−1 0.63% Expanded uncertainty U(k=2) 5.83E+04 Gy A−1 h−1 1.25% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.426E−02 Gy h−1 — 0.6 Table 6a Long-term stability kest 1.00 1 0.15 — Table 4 Average charge measurement with the transfer chamber Q̅std −2410.2 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −4.35E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibración factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3058 1 0.001 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for recombination effects krec 1.0005 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kd 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 0.3690 Calibration coefficient NKR 4.627E+05 Gy A−1 h−1 Combined uncertainty uc 2.92E+03 Gy A−1 h−1 0.63% Expanded uncertainty U(k=2) 5.83E+04 Gy A−1 h−1 1.25% a‘nC’, nominal nC. Table 6b. Uncertainty budget for the calibration coefficient NK̇R for SI A973052 transfer chamber in terms of K̇R using the Microselectron V2 source, measurements made by the SSDL-ININ at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.426E−02 Gy h−1 — 0.6 Table 6a Long-term stability kest 1.00 1 0.15 — Table 4 Average charge measurement with the transfer chamber Q̅std −2410.2 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −4.35E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibración factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3058 1 0.001 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for recombination effects krec 1.0005 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kd 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 0.3690 Calibration coefficient NKR 4.627E+05 Gy A−1 h−1 Combined uncertainty uc 2.92E+03 Gy A−1 h−1 0.63% Expanded uncertainty U(k=2) 5.83E+04 Gy A−1 h−1 1.25% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.426E−02 Gy h−1 — 0.6 Table 6a Long-term stability kest 1.00 1 0.15 — Table 4 Average charge measurement with the transfer chamber Q̅std −2410.2 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −4.35E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibración factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3058 1 0.001 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for recombination effects krec 1.0005 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kd 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 0.3690 Calibration coefficient NKR 4.627E+05 Gy A−1 h−1 Combined uncertainty uc 2.92E+03 Gy A−1 h−1 0.63% Expanded uncertainty U(k=2) 5.83E+04 Gy A−1 h−1 1.25% a‘nC’, nominal nC. Table 7. Uncertainty budget for the ratio RININ/CPHR. Chamber NKR 105/Gy A−1 h−1 ± uc% ININ ustb% NKR 105/Gy A−1 h−1 ± uc% CPHR RCPHR uc A002423 4.645 ± 0.49% 0.48 4.701 ± 0.46% 0.988 0.008 A941755 5.041 ± 0.49% 0.47 5.099 ± 0.46% 0.989 0.009 A973052 4.627 ± 0.49% 0.56 4.679 ± 0.46% 0.989 0.008 Birge’s average 0.989 0.005 Chamber NKR 105/Gy A−1 h−1 ± uc% ININ ustb% NKR 105/Gy A−1 h−1 ± uc% CPHR RCPHR uc A002423 4.645 ± 0.49% 0.48 4.701 ± 0.46% 0.988 0.008 A941755 5.041 ± 0.49% 0.47 5.099 ± 0.46% 0.989 0.009 A973052 4.627 ± 0.49% 0.56 4.679 ± 0.46% 0.989 0.008 Birge’s average 0.989 0.005 Table 7. Uncertainty budget for the ratio RININ/CPHR. Chamber NKR 105/Gy A−1 h−1 ± uc% ININ ustb% NKR 105/Gy A−1 h−1 ± uc% CPHR RCPHR uc A002423 4.645 ± 0.49% 0.48 4.701 ± 0.46% 0.988 0.008 A941755 5.041 ± 0.49% 0.47 5.099 ± 0.46% 0.989 0.009 A973052 4.627 ± 0.49% 0.56 4.679 ± 0.46% 0.989 0.008 Birge’s average 0.989 0.005 Chamber NKR 105/Gy A−1 h−1 ± uc% ININ ustb% NKR 105/Gy A−1 h−1 ± uc% CPHR RCPHR uc A002423 4.645 ± 0.49% 0.48 4.701 ± 0.46% 0.988 0.008 A941755 5.041 ± 0.49% 0.47 5.099 ± 0.46% 0.989 0.009 A973052 4.627 ± 0.49% 0.56 4.679 ± 0.46% 0.989 0.008 Birge’s average 0.989 0.005 Discussion The calibration coefficients obtained by the ININ and the CPHR are consistent with the experimental uncertainty and are considered satisfactory according to the value of the statistic En ≤ 1(16) (Table 3). However, all values of NK̇R determined by the SSDL-ININ are underestimated by −1.1% with respect to the values determined by the SSDL-CPHR (Table 3 and Figures 3 and 4). A possible explanation for this underestimation is that is due to an overestimation of the value of K̇R by both the SSDL-ININ and the SSDL-CPHR given the atmospheric pressure conditions of 774 hPa when the comparison was made. There are three arguments to consider for this possible cause of variation: The SI 90008 chambers with holders 70009 and 70016 need the use of an additional correction factor for kP,T(24, 25). Indeed, reference(26) for high-energy photons concludes that there is a breakdown in the kP,T factor for medium-sized cavities related to the non-equivalence of air with the chamber walls. In other words, this non-equivalence of air implies that the electronic equilibrium conditions are not met by the secondary electron field in the cavity, and so the application of the kP,T factor is no longer valid, since there is only a partial deposition of kinetic energy by the secondary electrons, the so-called ‘terminators’(24). The following factors further complicate this over-correction problem: The materials and size of the cavity, see Figure 2, which shows a sectioned drawing of the chamber. Backscatter from the aluminum wall of the chamber(24). To show the order and importance of the non-equivalence of the aluminum walls of the SI well chamber with the surrounding air, we calculate the ratio of (μρ̅)Al,air=1.0101 and (μenρ̅)Al,air=1.0860, where the sub-index Al, air means the ratio of the mean value of (μρ), calculated from the spectrum of the Ir 192 MicroSelectron V2 source(27). Indeed, the ratio of the mass coefficients is 1–8.6%, which means a correction in that interval for the most simplified case for the 192Ir spectrum. This correction is better understood if it is compared to the behavior of ionization chambers with air equivalent walls (C552 plastic) in X-ray dosimetry, where in fact there is no breakdown of the kP,T, see Figures 4 and 5 of reference(28) or the figures for the Exradin A2 chamber in reference(29). Therefore, we can conclude on a first approximation from these ratios that the variation in Figure 4(24), which shows the breakdown of the conventional kP,T factor, is due to the non-equivalence of the chamber walls to air. In other words, the electronic equilibrium conditions are not being met for this medium-sized cavity(24, 25); where, strictly, the butyrate should also be considered as part of the wall of the chamber. In agreement with the results of the regional comparison SIM RI (I)-K3 of orthovoltage x-rays for CCRI (I) radiation qualities(30), in general, ININ’s values of NK are underestimated by −1.2% with respect to those determined by the other laboratories located close to sea level. These low NK values are due to the underestimation of the air kerma rate values, when the conventional factor kP,T is applied to the ionization currents measured at ININ’s local air pressure (in the order of 710 hPa). In this comparison, the additional correction factors k′P,T;MC given in references(26, 28) are not applied. ININ reported that the correction factor k′P,T;MC should be applied in addition to kP,T because the SSDL-ININ is located 3000 m above the sea level. Nevertheless, an argument that leads us to think that the main cause of variation of the ratios, is the failure of kP,T. In fact, the results obtained in the SIM-K3 comparison for x-ray orthovoltage are also underestimated(30). These are expressed on the degree of equivalence DININ and its expanded uncertainty U, as −9.0 ± 16.0 mGy/Gy for 100 kV, −12.0 ± 16.0 mGy/Gy for 135 kV, −11.1 ± 16.1 mGy/Gy for 180 kV and −12.0 ± 16.1 mGy/Gy for 250 kV. The SSDL-ININ has two ionization chambers: the NE2611 s/n 176 and the Exradin A12 s/n 71931, both calibrated in terms of Dw and Ka for 60Co, at the RI section of the BIPM. The calibration certificate indicates that in the case of the NE2611 chamber (graphite walls) the ionization currents measured at air pressures in the order of 700 hPa, even when corrected by the conventional factor kP,T are underestimated by −0.2% (−2 parts per 1000 or −2 mGy/Gy) with respect to the measured current at normal pressure conditions (103.25 hPa) for 60Co energy. However, this effect is not observed for the Exradin A12 chamber whose walls are made of plastic C552(31, 32). On the other hand, in addition to the influence of the failure of the correction factor kP,T, there are other sources of variation that affect the values of the RININ/CPHR ratios, such as(33): The different traceability of the laboratories, as can be seen from the reference(34). However, as shown in Table 10, the values of the degree of equivalence Dij of +0.3 mG/Gy for the PTB and −1.1 mGy/Gy for the NPL are not enough to explain the variations in the order of 1% of the values of the calibration coefficients The use of different types of sources in the calibration of secondary standards and transfer chambers. Particularly, the PTB and this comparison used the same type of source but different to that used in the NPL (Table 1). Although, the NPL applies a correction factor for the source geometry ksg that corrects this variation(12, 35), which decreases the uncertainty in the determination of K̇R and the calibration factors determined by the ININ. The variation in the determination of the maximum response point (sweet spot), according to the analysis of the response curves implies a variation of 0.05–0.07%, which is not a significant cause explaining the variation of 1%. The contribution of the room scattering is kept to almost zero as each well chamber remained in the same position, at least 1 m from the walls, floor and ceiling during the course of the comparison(36). Figure 2. View largeDownload slide Schematic diagram of the SI HDR 1000 Plus chamber, showing the source holder volume, air-filled active volumes, collecting electrode and Al walls. Figure 2. View largeDownload slide Schematic diagram of the SI HDR 1000 Plus chamber, showing the source holder volume, air-filled active volumes, collecting electrode and Al walls. Additionally, to complete and demonstrate the validity of the later analysis, two means test sets are performed for the K̇R and NKR values, respectively(22): One-way ANOVA test (Tukey method) and one-way ANOM test of mean values for K̇R, α = 0.05%: H0:K̇R,CPHR=K̇R,ININ (6a) Therefore, according to the results of Table 8a and Figure 3, we reject H0 and conclude that the K̇R mean values determined by each laboratory are statistically significant, i.e. there is a cause of variation for this difference that should be investigated further. One-way ANOVA test (Tukey method) and one-way ANOM test for mean values of NKR: H0:NKR,CPHR=NKR,ININ (6b) Table 8a. One-way ANOVA: K̇R versus SSDL. Source DF SS MS F P SSDL 1 0.2647076 0.2647076 11973.37 0.000 Error 13 0.0002874 0.0000221 Total 14 0.2649950 Source DF SS MS F P SSDL 1 0.2647076 0.2647076 11973.37 0.000 Error 13 0.0002874 0.0000221 Total 14 0.2649950 Table 8a. One-way ANOVA: K̇R versus SSDL. Source DF SS MS F P SSDL 1 0.2647076 0.2647076 11973.37 0.000 Error 13 0.0002874 0.0000221 Total 14 0.2649950 Source DF SS MS F P SSDL 1 0.2647076 0.2647076 11973.37 0.000 Error 13 0.0002874 0.0000221 Total 14 0.2649950 Figure 3. View largeDownload slide Graph for the one-way ANOM test for the K̇R values by SSDL obtained in this comparison. Figure 3. View largeDownload slide Graph for the one-way ANOM test for the K̇R values by SSDL obtained in this comparison. Therefore, according to the results of Table 8b and Figure 4, we accept H0 and conclude that the mean values as determined by each laboratory are statistically equal. Table 8b. One-way ANOVA: NKR versus SSDL. Source DF SS MS F P SSDL 1 239625631 239625631 0.60 0.444 Error 28 11113892171 396924720 Total 29 11353517802 Source DF SS MS F P SSDL 1 239625631 239625631 0.60 0.444 Error 28 11113892171 396924720 Total 29 11353517802 Table 8b. One-way ANOVA: NKR versus SSDL. Source DF SS MS F P SSDL 1 239625631 239625631 0.60 0.444 Error 28 11113892171 396924720 Total 29 11353517802 Source DF SS MS F P SSDL 1 239625631 239625631 0.60 0.444 Error 28 11113892171 396924720 Total 29 11353517802 Figure 4. View largeDownload slide Graph for the one-way ANOM test for NKR by each SSDL obtained in this comparison. Figure 4. View largeDownload slide Graph for the one-way ANOM test for NKR by each SSDL obtained in this comparison. Therefore, although the values of K̇R are statistically different, the NKR values are statistically equal: how to explain this? Let us make the following heuristic analysis, aided by the following hypotheses: If the measurements with the HDR 1000 Plus and holder 70010 have the same overestimation as the measurements of the ionization currents made with holder 70009, (for the HDR 192Ir sources calibrated at 770 hPa this overestimation is 1.004(24)); the application of an additional factor k′P in the order to 0.996 is required. Now from Table 9, the value of k′P for the PTW chamber 3304 with holder H0379 T33002.1.009 is determined, assuming that hypothesis (6a) is valid for the corrected values of K̇R. Therefore, this PTW well chamber overestimates the values of K̇R by 1.6% (16 mGy/Gy), when the ionization currents are measured (at P ≈ 710 hPa) and corrected with the conventional correction factor kP. This deviation due to the overestimation of kP is greater than the one associated with the use of different sources: 3 mGy/Gy as assumed by the CPHR(9); or 4 mGy/Gy determined by the NPL(12, 35). However, in this comparison the former contribution of uncertainty in the case of CPHR does not apply; because, we are using a Microselectron V2 source, the same brand and model that PTB does, to calibrate this chamber (Table 1). However, it is necessary to determine and validate these k′P values and their uncertainties (for all atmospheric pressures), for example, with Monte Carlo techniques for both types of well chambers. Most importantly is to verify that the non-equivalence of the wall material to air is the main physical cause for the overestimation of K̇R. This is associated with the generation of the secondary field of electrons, and how these transport and deposit their energy in the internal and external air cavities of the well chamber(25). All SI chambers’ coefficients NK̇R calculated from the KṘ, determined by CPHR with the secondary standard PTW 3304-0154, are overestimated in 1.1%. This is because the behavior of the SI’s chambers does not cancel out the overresponse of the PTW chamber. However, when the SI chambers are calibrated with the secondary standard SI-9008-A963391, the overestimation effects are canceled between the SI transfer chambers and the SI standard. In fact, the NK̇R value of 4.67E + 05 Gy A−1 h−1 and 4.65E + 05 Gy A−1 h−1 reported by the PTB and the CPHR respectively, for the SI-90008-A973052 chamber calibrated close to sea level, the percentage differences are in the order of 0.4%. ININ’s NKR value obtained on this comparison for the same chamber is 4.63E5 Gy A−1 h−1 (Tables 3 and 6b). Finally, the null hypothesis of the mean test is accepted for NK̇R, because the SI 90008-A941755 chamber has a different sensitivity (lower volume) than the SI 90008-A973052 and A02423 transfer chambers. Therefore, the large variation of the average of the calibration coefficients, in order of 4% hiding the variation of 1% that exists between the determinations of NK̇R, made by the CPHR and the SSDL-ININ (Figure 5). Table 9. Parameters for the heuristic determination of k′P to PTW well chamber model 3304. Factor SSDL Unit CPHR ININ NKR 9.160E+05 4.597E+05 Gy h−1 A−1 I 20.451 40.307 nA kpol 1.0026 0.9999 1 krec 1.0005 1.0003 1 ksg — 1.0004 1 kPT 1.3059 1.3035 1 K̇R,Exp 0.0245 0.0243 Gy h−1 k′P 0.984 0.996 1 K̇R,Corr 0.0242 0.0242 Gy h−1 Factor SSDL Unit CPHR ININ NKR 9.160E+05 4.597E+05 Gy h−1 A−1 I 20.451 40.307 nA kpol 1.0026 0.9999 1 krec 1.0005 1.0003 1 ksg — 1.0004 1 kPT 1.3059 1.3035 1 K̇R,Exp 0.0245 0.0243 Gy h−1 k′P 0.984 0.996 1 K̇R,Corr 0.0242 0.0242 Gy h−1 View Large Table 9. Parameters for the heuristic determination of k′P to PTW well chamber model 3304. Factor SSDL Unit CPHR ININ NKR 9.160E+05 4.597E+05 Gy h−1 A−1 I 20.451 40.307 nA kpol 1.0026 0.9999 1 krec 1.0005 1.0003 1 ksg — 1.0004 1 kPT 1.3059 1.3035 1 K̇R,Exp 0.0245 0.0243 Gy h−1 k′P 0.984 0.996 1 K̇R,Corr 0.0242 0.0242 Gy h−1 Factor SSDL Unit CPHR ININ NKR 9.160E+05 4.597E+05 Gy h−1 A−1 I 20.451 40.307 nA kpol 1.0026 0.9999 1 krec 1.0005 1.0003 1 ksg — 1.0004 1 kPT 1.3059 1.3035 1 K̇R,Exp 0.0245 0.0243 Gy h−1 k′P 0.984 0.996 1 K̇R,Corr 0.0242 0.0242 Gy h−1 View Large Figure 5. View largeDownload slide Average NK̇R values of the transfer chambers of the SSDLs. Figure 5. View largeDownload slide Average NK̇R values of the transfer chambers of the SSDLs. Degree of equivalence Dij according to key comparison BIPM RI (I) K-8 An interesting aspect of this bilateral comparison is to try to link it with the results of the key comparison BIPM RI (I)-K8(7, 34). In particular, reference(37) establishes the relationship between the results of the i-th laboratory and the key comparison reference value (KCRV): Ri=NK,iNK,LINK⋅KLINKKBIPM=KiIi⋅ILINKKLINK⋅KLINKKBIPM, (7a) where the variance for the quotient Ri is given by the following equation: uR,i2=[ui2+uBIPM2−∑nfn2⋅(ui,n2+uBIPM,n2)]+ustab2+uLINK2 (7b) Finally, the degree of equivalence for the i-th laboratory is the difference: Di=Ri−1, (7c) and its expanded uncertainty is defined as follows: Ui=2⋅uR,i (7d) For pair-wise degrees of equivalence, Di,j=Di−Dj (8a) with variance: ui,j2=(ui2+uj2−∑nfn2⋅(ui,n2+uj,n2))+2ustab2 (8b) When using multiple transfer instruments (designated by subscript p), the expression for Ri becomes: Ri=∑pRi,pustab,p2∑p1ustab,p2 (9a) and, 1ustab2=∑p1ustab,p2 (9b) Therefore, in our case, the ratios Ri,j are defined as follows(7, 34, 37): RCPHR/BIPM=RCPHR/PTB⋅RPTB/BIPM, (10a) where: RCPHR/PTB=NCPHRNPTB, (10b) analogously, RININ/BIPM=RININ/NPL⋅RNPL/BIPM, (10c) RININ/NPL=NININNNPL, (10d) Now, the ratio RININ/BIPM/RCHPR/BIPM is calculated as follows: RININ/BIPM=RININ/CPHR⋅RCPHR/BIPM (10f) Then, with the results reported for Ri,j and ui,j in references(7, 9, 10) and generalized equations (8a, 8b, 9a, 9b) for the case of more than one transfer instrument and two link laboratories(37), we have the results of Table 10. Table 10. Degrees of equivalence for the bilateral comparison ININ CPHR. NMI/DIa Rij uij Dij Uij Date/reference mGy/Gy PTB/BIPM 1.0003 0.0099 +0.3 19.8 2011(31) NPL/BIPM 0.9989 0.0057 −1.1 11.4 2010(31) CPHR/PTB 1.0022 0.0035 +2.2 7.0 2014(9) CPHR/BIPM 1.0025 0.0105 +2.5 21.0 ININ/CPHR 0.9885 0.0049 −11.5 9.8 2016 ININ/BIPM 0.9910 0.0116 −9.0 23.2 NMI/DIa Rij uij Dij Uij Date/reference mGy/Gy PTB/BIPM 1.0003 0.0099 +0.3 19.8 2011(31) NPL/BIPM 0.9989 0.0057 −1.1 11.4 2010(31) CPHR/PTB 1.0022 0.0035 +2.2 7.0 2014(9) CPHR/BIPM 1.0025 0.0105 +2.5 21.0 ININ/CPHR 0.9885 0.0049 −11.5 9.8 2016 ININ/BIPM 0.9910 0.0116 −9.0 23.2 aNMI stands for National Metrology Institute and DI for Designated Institute. Table 10. Degrees of equivalence for the bilateral comparison ININ CPHR. NMI/DIa Rij uij Dij Uij Date/reference mGy/Gy PTB/BIPM 1.0003 0.0099 +0.3 19.8 2011(31) NPL/BIPM 0.9989 0.0057 −1.1 11.4 2010(31) CPHR/PTB 1.0022 0.0035 +2.2 7.0 2014(9) CPHR/BIPM 1.0025 0.0105 +2.5 21.0 ININ/CPHR 0.9885 0.0049 −11.5 9.8 2016 ININ/BIPM 0.9910 0.0116 −9.0 23.2 NMI/DIa Rij uij Dij Uij Date/reference mGy/Gy PTB/BIPM 1.0003 0.0099 +0.3 19.8 2011(31) NPL/BIPM 0.9989 0.0057 −1.1 11.4 2010(31) CPHR/PTB 1.0022 0.0035 +2.2 7.0 2014(9) CPHR/BIPM 1.0025 0.0105 +2.5 21.0 ININ/CPHR 0.9885 0.0049 −11.5 9.8 2016 ININ/BIPM 0.9910 0.0116 −9.0 23.2 aNMI stands for National Metrology Institute and DI for Designated Institute. The results shown in this table are preliminary, except those published by the BIPM in reference(34) are definitive and official, meaning our results are tentative and approximate and they must be validated according to the rules of the MRA(6). CONCLUSIONS According to the results obtained in this comparison, see Table 3, the SSDL-ININ has demonstrated its technical competence to determine K̇R, and the calibration of well chambers in the energy of the 192Ir for this quantity, within the declared uncertainty. However, the overestimation of −1.1% in K̇R and NKR values is caused by the breakdown of kPT for SSDL-ININ atmospheric conditions. A failure that as far as our knowledge is concerned is due to the electronic equilibrium conditions not being fulfilled, in our specific case for the medium-sized well chamber cavity, owing to the non-equivalence to air of its walls, according to references(26, 28). In addition, we relate these effects to the results of this bilateral comparison with those of key comparison BIPM RI (I)-K8(34), where we indirectly obtained a preliminary degree of equivalence DCPHR: (+2.5 ± Uij = 21.0) mGy/Gy for the SSDL-CPHR and a DININ: (−9.0 ± Uij = 23.2) mGy/Gy for the SSDL-ININ. Finally, it is concluded that the codes of practice for the determination of K̇R and NK̇R issued by the IAEA and the IPEM are equivalent. However, for the use of commercial well chambers in the North American, Mesoamerican (Mexican) and South American highlands, or locations with reduced atmospheric pressures (above 1000 m above sea level), it is required to either apply an additional correction factor k′PT, or to use secondary standard chambers designed with air equivalent walls, so as to accomplish the electronic equilibrium condition to reduce the breakdown of kP,T. ACKNOWLEDGEMENTS We wish to thank M.Sc. José Tendilla, manager of Nuclear Applications in Health of Instituto Nacional de Investigaciones Nucleares for the funding of project ININ-ME-06-2016 and the facilities provided for the completion of this work. We are grateful to Dr Mata and M.Sc. Omar Hernandez-Oviedo from the Radiotherapy Unit of the Cancer Center at the American British Cowdray Medical Center; and Dr Aida Mota and M.Sc. Miguel Rodríguez at the Radiotherapy Subdirection of the Instituto Nacional de Cancerología, whose invaluable support directly and indirectly contributed in the development of this comparison. Finally, we appreciate the generous comments of the referee who made us notice the implications of the non-equivalence to air of the well chamber walls. REFERENCES 1 https://www.gob.mx/salud/acciones-y-programas/informacion-estadistica (In Spanish, last accessed 2018-03-26). 2 https://www.cancer.org/cancer/cervical-cancer/treating/radiation.html (In Spanish, last accessed 2018-03-26). 3 DeWerd , L. A. , Ibbott , G. S. , Meigooni , A. S. , Mitch , M. G. , Rivard , M. J. , Stump , K. E. , Thomadsen , B. R. and Venselaar , J. L. A dosimetric uncertainty analysis for photon-emitting brachytherapy sources: report of AAPM Task Group No. 138 and GEC-ESTRO . 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L. Cuban laboratory proficiency test for calibration of well-type chambers using two types of HDR192Ir sources, E2-CN182, paper 018. In: Book of Extended Synopses of Standards, Applications and Quality Assurance in Medical Radiation Dosimetry (IDOS), Vienna, Austria ( 2010 ). 11 Di Prinzio , R. and DeAlmeida , CE Air kerma standard for calibration of well-type chambers in Brazil using 192Ir HDR sources and its traceability . Med. Phys. 36 ( 3 ), 95 ( 2009 ). Google Scholar CrossRef Search ADS PubMed 12 Bidmead , A. M. , Sander , T. , Locks , S. M. , Lee , C. D. , Aird , E. G. A. , Nutbrown , R. F. and Flynn , A. The IPEM code of practice for determination of the reference air kerma rate for HDR 192Ir brachytherapy sources based on the NPL air kerma standard . Phys. Med. Biol. 55 , 3145 – 3159 ( 2010 ). Google Scholar CrossRef Search ADS PubMed 13 Stump , K. E. , DeWerd , L. A. , Micka , J. A. and Anderson , D. R. Calibration of new high dose rate 192Ir sources . Med. 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BIPM Certificate N° 11 for the study and calibration in a 60Co gamma-ray beam of the ionization chamber Exradin A12, serial number 71931, of the Instituto Nacional de Investigaciones Nucleares (ININ), Salazar , Mexico. Sèvres ( 2008 ). 33 Douysset , G. , Sander , T. , Gouriou , J. and Nutbrown , R. F. Comparison of air kerma standards of LNE–LNHB and NPL for 192Ir HDR brachytherapy sources: EUROMET project no 814 . Phys. Med. Biol. 53 , N85 – N97 ( 2008 ). Google Scholar CrossRef Search ADS PubMed 34 http://kcdb.bipm.org/appendixB/appbresults/bipm.ri(i)-k8/RI(I)-K8_dec15.pdf (last accessed 2018-03-26). 35 Shipley , D. R. , Sander , T. and Nutbrown , R. F. Source geometry factors for HDR 192Ir brachytherapy secondary standard well-type ionization chamber calibrations . Phys. Med. Biol. 60 , 2573 – 2586 ( 2015 ). Google Scholar CrossRef Search ADS PubMed 36 Chang , L. , Ho , S. , Chui , C. , Lee , J. , Du , Y. and Chen , T. A statistical approach to infer the minimum setup distance of a well chamber to the wall or to the floor for 192Ir HDR calibration . Med. Phys. 35 , 2214 – 2217 ( 2008 ). Google Scholar CrossRef Search ADS PubMed 37 Burns , D. T. and Allisy-Roberts , P. J. The evaluation of degrees of equivalence in regional dosimetry comparisons. CCRI (I) 07-04 (BIPM, Paris) ( 2007 ). © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Radiation Protection Dosimetry Oxford University Press

PROFICIENCY TEST OF THE SSDL-ININ-MEXICO FOR THE CALIBRATION OF WELL-TYPE CHAMBERS WITH HDR 192IR SOURCES USING TWO DIFFERENT DOSIMETRY CODES OF PRACTICE FOR THE DETERMINATION OF REFERENCE AIR KERMA RATE K ̇ R

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Abstract

Abstract The results of the comparison between SSDL-ININ and SSDL-CPHR (pilot laboratory) demonstrates the competence of the SSDL-ININ for the performance of the K̇R in 192Ir. The RININ/CHPR ratio for the calibration coefficients is 0.989 ± 0.005. The comparison uses three SI-HDR 1000-Plus as transfer chambers, series: A02423, A941755 and A973052. CPHR used a secondary standard PTW 3304 chamber, s/n 154, calibrated at PTB and ININ employed a secondary standard SI-90008 s/n A963391, calibrated at NPL. To determine K̇R, the SSDL-CPHR used the IAEA TEC-DOC-1274 and the SSDL-ININ used the IPEM (UK) code of practice. The latter uses a correction factor by source’s geometry, ksg. The results show that both codes are equivalent; however, for the use of well chambers in the highlands or in locations with reduced atmospheric pressure, it is needed to apply an additional factor k′P, or, to design a well chamber with air-equivalent walls for the application of the conventional kPT. INTRODUCTION In Latin America, uterine cervical cancer is the second cause of death among women(1). This neoplasm is usually treated with surgery and/or high and low dose rate brachytherapy (BT), with 192Ir sources and sets of 137Cs sources, respectively(2). However, to achieve success in tumor control using external beam radiotherapy (RT) and/or BT, the restrictions on accuracy and precision are that the absorbed dose given to the tumoral volume has an expanded uncertainty U(k=2)<5% for RT and U(k=2)<10% for BT(3). To guarantee the fullfilment of these and other quality control constrictions, the IAEA/WHO SSDL network of dosimetry laboratories provide calibration services and dosimetry support to the RT centers in each country, where them are located(4). Requirements of the ISO 17025 for comparisons On the other hand, a general requirement of the ISO 17025 is that calibration laboratories demonstrate their technical competence through comparisons between laboratories and/or proficiency tests(5). For the primary laboratories of the National Institutes of Metrology and Institutes designated under the CIPM Mutual Recognition Agreement(6), these comparisons, in the case of high dose rate BT, correspond to the key comparison BIPM RI(I)-K8, for rate of reference air kerma ( KṘ) with 192Ir sources(7). In the case of SSDL’s, however, these comparisons are usually bilateral comparisons, where the pilot laboratory is a primary laboratory(8–10). There are also bilateral comparisons between SSDL’s such as the one conducted between ADCL of the U. Wisconsin and the Laboratory of Radiological Sciences of the Catholic University of Rio de Janeiro, Brazil; where the calibration of the source is performed using the 7-point method, and a well chamber is used as the transfer chamber(11). However, an underlying problem in these comparisons is that the secondary standard is calibrated with a source type 192Ir at the primary laboratory with a primary standard chamber, and the Hospital or the SSDL use other similar type of source, but with different geometry, design and construction (Table 1)(9, 10). Table 1. Characteristics of the 192Ir sources used in bilateral comparison ININ-CPHR. Source type Active core Encapsulation Location Isotope Length (mm) Diameter (mm) Stain steel Thickness (mm) Outer diameter (mm) Length (mm) Microselectron V2 192Ir 3.60 0.65 AISI316 0.125 0.90 4.50 PTB, Braunschweig, DECancer Center, Hospital ABC, Mexico City, MX Isodose control Flexisource 192Ir 3.50 0.60 AISI316L 0.20 0.86 4.60 NPL, Teddington, UK Source type Active core Encapsulation Location Isotope Length (mm) Diameter (mm) Stain steel Thickness (mm) Outer diameter (mm) Length (mm) Microselectron V2 192Ir 3.60 0.65 AISI316 0.125 0.90 4.50 PTB, Braunschweig, DECancer Center, Hospital ABC, Mexico City, MX Isodose control Flexisource 192Ir 3.50 0.60 AISI316L 0.20 0.86 4.60 NPL, Teddington, UK Table 1. Characteristics of the 192Ir sources used in bilateral comparison ININ-CPHR. Source type Active core Encapsulation Location Isotope Length (mm) Diameter (mm) Stain steel Thickness (mm) Outer diameter (mm) Length (mm) Microselectron V2 192Ir 3.60 0.65 AISI316 0.125 0.90 4.50 PTB, Braunschweig, DECancer Center, Hospital ABC, Mexico City, MX Isodose control Flexisource 192Ir 3.50 0.60 AISI316L 0.20 0.86 4.60 NPL, Teddington, UK Source type Active core Encapsulation Location Isotope Length (mm) Diameter (mm) Stain steel Thickness (mm) Outer diameter (mm) Length (mm) Microselectron V2 192Ir 3.60 0.65 AISI316 0.125 0.90 4.50 PTB, Braunschweig, DECancer Center, Hospital ABC, Mexico City, MX Isodose control Flexisource 192Ir 3.50 0.60 AISI316L 0.20 0.86 4.60 NPL, Teddington, UK Proposed solution on the use of different sources for the calibration process at a SSDL and/or hospital This problem is solved by: The use at the SSDL or hospital of a calibration source equal to the one used at the primary laboratory. By means of a dosimetry code of practice for K̇R that considers a correction factor for the geometric differences of the calibration sources ksg(12). Additionally, there is another approximation that introduces a component of uncertainty that considers the variation of the source types(10, 11, 13); however, this does not solve the problem. Therefore, the aim of this work is to demonstrate the technical competence of the SSDL-ININ-México for its calibration and measurement capability (CMC) in the K̇R quantity for 192Ir sources, for the calibration of well chambers, (with the use of the dosimetry code of practice developed by the IPEM that considers a source geometry correction factor(12)), by a bilateral comparison with the SSDL-CPHR-Cuba. (Which in turn employs the IAEA calibration codes of practice TEC 1274, and adding an uncertainty component by using different design sources on the calibration process(14).) In particular, the SSDL-CPHR-Cuba is the pilot laboratory given its experience in bilateral comparisons(9, 10); this SSDL uses the secondary standard PTW model 33004 serial 0154 (with a nominal volume 116 cm3), calibrated at the PTB in 2013. The secondary standard of the SSDL-ININ is a Standard Imaging model HDR-100 Plus s/n A963391 (with a nominal volume 245 cm3) calibrated at the NPL in the year 2016; both chambers are calibrated in terms of KR, see Tables 1 and 4 for a detailed description of the sources, chambers and holders used. The comparison is performed at the Radiotherapy Department on the Cancer Center of the Hospital ABC, located in Mexico City, which has a MicroSelectron source V2 (Table 1). The laboratories have agreed to evaluate the results obtained using the normalized error value, En, as recommended in ISO/IEC 17043(15). In the next section, the dosimetry codes of practice employed on the calibration of radioactive sources and the well chamber are discussed. DOSIMETRY CODES OF PRACTICE FOR THE CALIBRATION OF WELL CHAMBERS IN TERMS OF K̇R There are two basic techniques for the calibration of high and low dose rate BT sources in terms of K̇R, which are briefly described below(14). The reader can find more details in the review article(16). Determination of K̇R with a cavity ionization chamber at the reference distance The basic formula for determining K̇R from the air kerma rate is given by the following equation(14): K̇R=NK̇R⋅(Q/t)⋅kel⋅kP,T⋅kpol⋅krec⋅kscat⋅katt⋅kn⋅[ddr]2 (1) where K̇R, is the reference kerma rate [Gy s−1] defined in references(17, 18). NK̇R is the calibration factor for a standard chamber calibrated in air kerma for 192Ir [Gy/C](11–14, 16, 19, 20). Q, integrated charge [C]. t, integration time [s]. kel, kP,T, kpol, krec, kscat, katt, kn, d and dr are the calibration factor of the electrometer; corrections for atmospheric pressure and temperature; polarization; recombination losses; scattering; attenuation; a non-uniformity correction factor that accounts for the non-uniform electron fluence within the air cavity, the distance between the center of the source and the center of the ionization chamber; and the reference distance of 1 m, respectively. Determination of K̇R with a well chamber There are two basic codes of practice for determining the K̇R using a well chamber: The general code of practice without correction for the difference between the geometry of the calibration source in relation to the source to be calibrated(14). K̇R=NK̇R⋅(Q/t)⋅kel⋅kP,T⋅krec⋅kdec (2a) Here, K̇R is the air kerma reference rate; NKR is the calibration factor of the well chamber (determined with a calibrated source); Q is the charge measurement [C]; T is the integration time [s]. The code of practice where the correction factor for differences in the geometry of the calibration source and the source to be calibrated ksg(12), in Eq. (2b) is applied: K̇R=NK̇R⋅(Q/t)⋅kel⋅kP,T⋅krec⋅kdec⋅ksg, (2b) here, each component was defined in Eqs. (1) and (2a). Calibration of a well chamber in terms of K̇R The expression for the calibration of a well chamber is as follows(14): NK̇R=K̇R(Q/t)⋅kel⋅kPT⋅krec⋅kdec, (3) where, each term has already been defined previously. Once the calibration coefficients for each laboratory are determined from (3), the competence of the SSDL-ININ is evaluated according to the ISO/IEC 17043 Conformity assessment—General requirements for proficiency testing(15), the normalized error En is one of the statistics proposed for evaluating the performance of a comparison, in particular: En=NK,ININ−NK,CPHRUK,ININ2+UK,CPHR2 (4) where NK,ININ is the calibration coefficient reported by ININ. NK,CPHR is the calibration coefficient reported by CHPR. UK,ININ(k=2) is the expanded standard uncertainty reported by the ININ, for a 95% confidence interval. UK,CHPR(k=2) is the expanded standard uncertainty reported by the CPHR, for a 95% confidence interval. This statistic normalizes the difference of values of the calibration coefficients reported by both laboratories with respect to their associated expanded uncertainties. Experimental conditions and procedure for the bilateral comparison The comparison exercise considers two parts: A set of specific experimental conditions for the standard and transfer chambers. A procedure for realizing the comparison. Experimental conditions for the comparison Table 2 summarizes the standard and transfer well chambers used during the comparison. An important condition is that each chamber has its own (one or several) source holders. The calibration factor refers to the integral instrument, i.e. chamber plus holder. For the determination of the K̇R using the secondary standard instrument, the holder used at the Primary Standard Dosimetry Laboratory during calibration was applied. In a similar way, for the calibration of the transfer chamber, its own source holder was used. Since, a change of holder than the one used in the well chamber calibration at the primary or secondary laboratory implies a change in its calibration factor(21). Table 2. The standards and transfer well chambers used in the bilateral comparison ININ-CPHR. SSDLa Hierarchy/traceability Brand Model Serial HV/Collected charge sign Holder Hmax/mm Catheter length/mm Step/mm Electrometer/Traceability CPHR Secondary Standard/PTB PTW 33004 00154 +400/ Positive H0379 T33002.1.009 40/ 1382 2.5 Keithley 6517B, s/n 1287710 CENAM Transfer SIa HDR 1000 Plus (90008) A973052 +300/ Negative 70010 A973052 47.5/ 1275 2.5 SI, MAX 4000, s/n F092884 CENAM ININ Secondary Standard/NPL SI HDR 1000 Plus (90008) A963391 +300/ Negative 70010 A963391 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM Transfer SI HDR 1000 Plus (90008) A941755 +300/ Negative 70010 A941755 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM SSDLa Hierarchy/traceability Brand Model Serial HV/Collected charge sign Holder Hmax/mm Catheter length/mm Step/mm Electrometer/Traceability CPHR Secondary Standard/PTB PTW 33004 00154 +400/ Positive H0379 T33002.1.009 40/ 1382 2.5 Keithley 6517B, s/n 1287710 CENAM Transfer SIa HDR 1000 Plus (90008) A973052 +300/ Negative 70010 A973052 47.5/ 1275 2.5 SI, MAX 4000, s/n F092884 CENAM ININ Secondary Standard/NPL SI HDR 1000 Plus (90008) A963391 +300/ Negative 70010 A963391 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM Transfer SI HDR 1000 Plus (90008) A941755 +300/ Negative 70010 A941755 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM aStandard imaging. Table 2. The standards and transfer well chambers used in the bilateral comparison ININ-CPHR. SSDLa Hierarchy/traceability Brand Model Serial HV/Collected charge sign Holder Hmax/mm Catheter length/mm Step/mm Electrometer/Traceability CPHR Secondary Standard/PTB PTW 33004 00154 +400/ Positive H0379 T33002.1.009 40/ 1382 2.5 Keithley 6517B, s/n 1287710 CENAM Transfer SIa HDR 1000 Plus (90008) A973052 +300/ Negative 70010 A973052 47.5/ 1275 2.5 SI, MAX 4000, s/n F092884 CENAM ININ Secondary Standard/NPL SI HDR 1000 Plus (90008) A963391 +300/ Negative 70010 A963391 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM Transfer SI HDR 1000 Plus (90008) A941755 +300/ Negative 70010 A941755 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM SSDLa Hierarchy/traceability Brand Model Serial HV/Collected charge sign Holder Hmax/mm Catheter length/mm Step/mm Electrometer/Traceability CPHR Secondary Standard/PTB PTW 33004 00154 +400/ Positive H0379 T33002.1.009 40/ 1382 2.5 Keithley 6517B, s/n 1287710 CENAM Transfer SIa HDR 1000 Plus (90008) A973052 +300/ Negative 70010 A973052 47.5/ 1275 2.5 SI, MAX 4000, s/n F092884 CENAM ININ Secondary Standard/NPL SI HDR 1000 Plus (90008) A963391 +300/ Negative 70010 A963391 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM Transfer SI HDR 1000 Plus (90008) A941755 +300/ Negative 70010 A941755 47.5/ 1275 2.5 SI, MAX 4000 s/n F092884 CENAM aStandard imaging. Measurement protocol for the comparison It consists of two stages, namely: Determination of K̇R with the secondary standard chambers. This has seven steps, which are: Measurements of stability of the secondary standard chambers before comparison. Leakage current measurements for said chambers. Determination of the point of maximum response (sweet spot). Five charge measurements for an integration time of 60 s for the SI (Standard Imaging) chambers and 10 measurements with an integration time of 30 s for the PTW chamber, with nominal operating voltage (100%). Five charge measurements for an integration time of 60 s for SI chambers and 10 measurements with an integration time of 30 s for PTW chamber, with operating voltage of 50%, to determine krec. Five charge measurements for an integration time of 60 s for SI chambers and 10 measurements with an integration time of 30 s for the PTW chamber, with operating voltage of −100%, to determine kpol. Stability measurements of the secondary standard chambers after comparison. Calibration of the SI transfer chamber, which consists of six steps, similar to the previous ones except for the polarization correction, see Eq. (3). As mentioned, the comparison took place at the Cancer Center of the Hospital ABC located in Mexico City; a MicroSelectron V2 source was used (Table 1). The atmospheric conditions during the comparison were: Temperature on the chamber cavity 20 ± 1°C measured with a Fluke thermometer model 1521 s/n A68868 with a Hart scientific thermistor, model 5611T serial A881420; calibrated at CENAM (Mexico). Atmospheric pressure: from 773.7 to 775.4 hPa, measured with a Vaisala digital barometer, model PTB 330 serial F2910009, calibrated at CENAM. The relative humidity during the comparison is maintained at 50%. RESULTS AND DISCUSSION Values of the calibration coefficients, expanded uncertainties and associated statistics Table 3 shows the values for K̇R calculated with Eq. (2a) by the CPHR and with Eq. (2b) for the ININ, the calibration coefficient NK̇R is determined by Eq. (3), Δ% is the difference percentage between the values of NK̇R with respect to the CHPR’s value; where the quotient RININ/CPHR is defined as follows: RININ/CPHR=NKRININNKRCPHR=K̇R,ININIININ⋅ICPHRK̇R,CPHR, (5) Table 3. Summary of the results of the bilateral comparison ININ CPHR for K̇R to 192Ir. Well chamber NK̇R 105/Gy A−1 h−1 ± U% (k = 2) K̇R/mGy h−1 ± U% (k = 2)a Δ% RININ/CPHR±uc En ININ CPHR ININ (NPL) CPHR (PTB) A002423 4.645 ± 1.25% 4.701 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.19 0.988 ± 0.008 0.440 A941755 5.041 ± 1.25% 5.099 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.14 0.989 ± 0.009 0.393 A973052 4.627 ± 1.25% 4.679 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.11 0.989 ± 0.008 0.384 Well chamber NK̇R 105/Gy A−1 h−1 ± U% (k = 2) K̇R/mGy h−1 ± U% (k = 2)a Δ% RININ/CPHR±uc En ININ CPHR ININ (NPL) CPHR (PTB) A002423 4.645 ± 1.25% 4.701 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.19 0.988 ± 0.008 0.440 A941755 5.041 ± 1.25% 5.099 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.14 0.989 ± 0.009 0.393 A973052 4.627 ± 1.25% 4.679 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.11 0.989 ± 0.008 0.384 aThe K̇R for source of Microselectron V2 is normalized to 2016 08 22, 18:53 central time of Mexico. Table 3. Summary of the results of the bilateral comparison ININ CPHR for K̇R to 192Ir. Well chamber NK̇R 105/Gy A−1 h−1 ± U% (k = 2) K̇R/mGy h−1 ± U% (k = 2)a Δ% RININ/CPHR±uc En ININ CPHR ININ (NPL) CPHR (PTB) A002423 4.645 ± 1.25% 4.701 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.19 0.988 ± 0.008 0.440 A941755 5.041 ± 1.25% 5.099 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.14 0.989 ± 0.009 0.393 A973052 4.627 ± 1.25% 4.679 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.11 0.989 ± 0.008 0.384 Well chamber NK̇R 105/Gy A−1 h−1 ± U% (k = 2) K̇R/mGy h−1 ± U% (k = 2)a Δ% RININ/CPHR±uc En ININ CPHR ININ (NPL) CPHR (PTB) A002423 4.645 ± 1.25% 4.701 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.19 0.988 ± 0.008 0.440 A941755 5.041 ± 1.25% 5.099 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.14 0.989 ± 0.009 0.393 A973052 4.627 ± 1.25% 4.679 ± 2.60% 24.256 ± 1.20% 24.537 ± 2.58% −1.11 0.989 ± 0.008 0.384 aThe K̇R for source of Microselectron V2 is normalized to 2016 08 22, 18:53 central time of Mexico. Finally, En is calculated with Eq. (4). The leakage currents measured during the comparison, along with the long and short-term stability reported by each laboratory are summarized in Table 4. Table 4. Summary of leakage currents and short and long-term stability of the standard and transfer well chambers participating on the bilateral comparison CHPR and ININ. SSDL Well chamber/hierarchy Ileak/A Stability % Reference Short term Long term CPHR PTW 00154 Secondary 2.9E−14 0.024 0.29 (9) SI A973052 Transfer −7.3E−14 0.004 0.14 (9) ININ SI A963391 Secondary 22E−14 0.013 0.17 CC IMR RS SI A002423 Transfer −5.6E−14 0.013 0.17 CC IMR RS SI A941755 Transfer −7.2E−14 0.013 0.13 CC IMR RS SSDL Well chamber/hierarchy Ileak/A Stability % Reference Short term Long term CPHR PTW 00154 Secondary 2.9E−14 0.024 0.29 (9) SI A973052 Transfer −7.3E−14 0.004 0.14 (9) ININ SI A963391 Secondary 22E−14 0.013 0.17 CC IMR RS SI A002423 Transfer −5.6E−14 0.013 0.17 CC IMR RS SI A941755 Transfer −7.2E−14 0.013 0.13 CC IMR RS Table 4. Summary of leakage currents and short and long-term stability of the standard and transfer well chambers participating on the bilateral comparison CHPR and ININ. SSDL Well chamber/hierarchy Ileak/A Stability % Reference Short term Long term CPHR PTW 00154 Secondary 2.9E−14 0.024 0.29 (9) SI A973052 Transfer −7.3E−14 0.004 0.14 (9) ININ SI A963391 Secondary 22E−14 0.013 0.17 CC IMR RS SI A002423 Transfer −5.6E−14 0.013 0.17 CC IMR RS SI A941755 Transfer −7.2E−14 0.013 0.13 CC IMR RS SSDL Well chamber/hierarchy Ileak/A Stability % Reference Short term Long term CPHR PTW 00154 Secondary 2.9E−14 0.024 0.29 (9) SI A973052 Transfer −7.3E−14 0.004 0.14 (9) ININ SI A963391 Secondary 22E−14 0.013 0.17 CC IMR RS SI A002423 Transfer −5.6E−14 0.013 0.17 CC IMR RS SI A941755 Transfer −7.2E−14 0.013 0.13 CC IMR RS In Table 4 and Figure 1, CC I-MR-R/S refers to the I-MR R/S control charts(22) for the SI secondary chamber HDR100 Plus s/n A963391, corresponding to 29 determinations of K̇R performed from March 2011 to December 2016 for the Amersham CDCSM 137Cs source, serial EB811. Figure 1. View largeDownload slide I-MR-R/S Control chart for K̇R measurements made with SI A963391 transfer well chamber and the Amersham CDCSM4 137Cs source serial EB811, where MR gives the long-term stability(22). Figure 1. View largeDownload slide I-MR-R/S Control chart for K̇R measurements made with SI A963391 transfer well chamber and the Amersham CDCSM4 137Cs source serial EB811, where MR gives the long-term stability(22). On the other hand, the uncertainty budget for the combined uc and expanded U uncertainties reported in Table 3, are detailed in Tables 5–7; where such uncertainties are calculated with the BIPM-ISO Guide(23). Table 5a. Uncertainty budget for the calibration of the Microselectron V2 source in terms of K̇R using the secondary standard well chamber PTW 3304 serial 0154, measurements made by the SSDL-CPHR at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 9.16E+05 Gy/(A.h) — 1.25 Certificate PTB 6.22–29/13K Long-term stability kest 1.00 1 0.29 — Table 4 Average charge measurement with the standard Q̅std 613.47 ‘nC’a 0.024 — n = 10 Average leak charge Q̅l,std 1.21E−03 ‘nC’a 0.0001 — Integration time 30 s Integration time t 30 s — 0.001 Electrometer calibration factor kel 1.000074 nC/‘nC’a — 0.0005 Keithley 6517B, s/n 1287710 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3059 1 0.01 0.05 P = 773.94 ± 0.06 hPa, T = 19.250 ± 0.006°C Correction factor for polarity effects kpol 1.0026 1 0.04 — V1 = +400 V, V2 = −400 V Correction factor for recombination effects krec 1.0005 1 0.04 — V1/2 = +200 V Correction factor for radioactive decay kdec 1.00002 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0869 1.5656 Reference air kerma rate K̇R 2.454E−02 Gy h−1 Combined uncertainty uc 3.15E−04 G h−1 1.29% Expanded uncertainty U(k=2) 6.30E−04 Gy h−1 2.58% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 9.16E+05 Gy/(A.h) — 1.25 Certificate PTB 6.22–29/13K Long-term stability kest 1.00 1 0.29 — Table 4 Average charge measurement with the standard Q̅std 613.47 ‘nC’a 0.024 — n = 10 Average leak charge Q̅l,std 1.21E−03 ‘nC’a 0.0001 — Integration time 30 s Integration time t 30 s — 0.001 Electrometer calibration factor kel 1.000074 nC/‘nC’a — 0.0005 Keithley 6517B, s/n 1287710 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3059 1 0.01 0.05 P = 773.94 ± 0.06 hPa, T = 19.250 ± 0.006°C Correction factor for polarity effects kpol 1.0026 1 0.04 — V1 = +400 V, V2 = −400 V Correction factor for recombination effects krec 1.0005 1 0.04 — V1/2 = +200 V Correction factor for radioactive decay kdec 1.00002 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0869 1.5656 Reference air kerma rate K̇R 2.454E−02 Gy h−1 Combined uncertainty uc 3.15E−04 G h−1 1.29% Expanded uncertainty U(k=2) 6.30E−04 Gy h−1 2.58% a‘nC’, nominal nC. Table 5a. Uncertainty budget for the calibration of the Microselectron V2 source in terms of K̇R using the secondary standard well chamber PTW 3304 serial 0154, measurements made by the SSDL-CPHR at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 9.16E+05 Gy/(A.h) — 1.25 Certificate PTB 6.22–29/13K Long-term stability kest 1.00 1 0.29 — Table 4 Average charge measurement with the standard Q̅std 613.47 ‘nC’a 0.024 — n = 10 Average leak charge Q̅l,std 1.21E−03 ‘nC’a 0.0001 — Integration time 30 s Integration time t 30 s — 0.001 Electrometer calibration factor kel 1.000074 nC/‘nC’a — 0.0005 Keithley 6517B, s/n 1287710 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3059 1 0.01 0.05 P = 773.94 ± 0.06 hPa, T = 19.250 ± 0.006°C Correction factor for polarity effects kpol 1.0026 1 0.04 — V1 = +400 V, V2 = −400 V Correction factor for recombination effects krec 1.0005 1 0.04 — V1/2 = +200 V Correction factor for radioactive decay kdec 1.00002 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0869 1.5656 Reference air kerma rate K̇R 2.454E−02 Gy h−1 Combined uncertainty uc 3.15E−04 G h−1 1.29% Expanded uncertainty U(k=2) 6.30E−04 Gy h−1 2.58% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 9.16E+05 Gy/(A.h) — 1.25 Certificate PTB 6.22–29/13K Long-term stability kest 1.00 1 0.29 — Table 4 Average charge measurement with the standard Q̅std 613.47 ‘nC’a 0.024 — n = 10 Average leak charge Q̅l,std 1.21E−03 ‘nC’a 0.0001 — Integration time 30 s Integration time t 30 s — 0.001 Electrometer calibration factor kel 1.000074 nC/‘nC’a — 0.0005 Keithley 6517B, s/n 1287710 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3059 1 0.01 0.05 P = 773.94 ± 0.06 hPa, T = 19.250 ± 0.006°C Correction factor for polarity effects kpol 1.0026 1 0.04 — V1 = +400 V, V2 = −400 V Correction factor for recombination effects krec 1.0005 1 0.04 — V1/2 = +200 V Correction factor for radioactive decay kdec 1.00002 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0869 1.5656 Reference air kerma rate K̇R 2.454E−02 Gy h−1 Combined uncertainty uc 3.15E−04 G h−1 1.29% Expanded uncertainty U(k=2) 6.30E−04 Gy h−1 2.58% a‘nC’, nominal nC. Table 5b. Uncertainty budget for the calibration coefficient NK̇R of SI A941755 transfer chamber in terms of K̇R using the Microselectron V2, measurements realized by the SSDL-CPHR at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.454E−02 Gy h−1 — 1.29 Table 5a Long-term stability kest 1.00 1 — 0.15 Table 4 Average charge measurement with the transfer chamber Q̅std −2211.9 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −3.33E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3049 1 0.004 0.05 P = 774.66 ± 0.03 hPa, T = 19.312 ± 0.001°C Correction factor for recombination effects krec 1.0007 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kdec 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 1.6632 Calibration coefficient NKR 5.099E+05 Gy A−1 h−1 Combined uncertainty uc 6.620E+03 Gy A−1 h−1 1.30% Expanded uncertainty U(k=2) 1.324E+04 Gy A−1 h−1 2.60% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.454E−02 Gy h−1 — 1.29 Table 5a Long-term stability kest 1.00 1 — 0.15 Table 4 Average charge measurement with the transfer chamber Q̅std −2211.9 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −3.33E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3049 1 0.004 0.05 P = 774.66 ± 0.03 hPa, T = 19.312 ± 0.001°C Correction factor for recombination effects krec 1.0007 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kdec 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 1.6632 Calibration coefficient NKR 5.099E+05 Gy A−1 h−1 Combined uncertainty uc 6.620E+03 Gy A−1 h−1 1.30% Expanded uncertainty U(k=2) 1.324E+04 Gy A−1 h−1 2.60% a‘nC’, nominal nC. Table 5b. Uncertainty budget for the calibration coefficient NK̇R of SI A941755 transfer chamber in terms of K̇R using the Microselectron V2, measurements realized by the SSDL-CPHR at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.454E−02 Gy h−1 — 1.29 Table 5a Long-term stability kest 1.00 1 — 0.15 Table 4 Average charge measurement with the transfer chamber Q̅std −2211.9 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −3.33E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3049 1 0.004 0.05 P = 774.66 ± 0.03 hPa, T = 19.312 ± 0.001°C Correction factor for recombination effects krec 1.0007 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kdec 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 1.6632 Calibration coefficient NKR 5.099E+05 Gy A−1 h−1 Combined uncertainty uc 6.620E+03 Gy A−1 h−1 1.30% Expanded uncertainty U(k=2) 1.324E+04 Gy A−1 h−1 2.60% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.454E−02 Gy h−1 — 1.29 Table 5a Long-term stability kest 1.00 1 — 0.15 Table 4 Average charge measurement with the transfer chamber Q̅std −2211.9 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −3.33E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3049 1 0.004 0.05 P = 774.66 ± 0.03 hPa, T = 19.312 ± 0.001°C Correction factor for recombination effects krec 1.0007 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kdec 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 1.6632 Calibration coefficient NKR 5.099E+05 Gy A−1 h−1 Combined uncertainty uc 6.620E+03 Gy A−1 h−1 1.30% Expanded uncertainty U(k=2) 1.324E+04 Gy A−1 h−1 2.60% a‘nC’, nominal nC. Table 6a. Uncertainty budget for the calibration of the Microselectron V2 source in terms of K̇R using the secondary standard SI 90008 well chamber serial A963391, measurements realized by the SSDL-ININ at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 127.7 Gy C-1 — 0.4 Certificate NPL 2016030013-1 Long-term stability kest 1.00 1 0.17 — Table 4 Average charge measurement with the standard Q̅std −2418.86 ‘nC’a 0.004 — n = 10 Average leak charge Q̅l,std −3.00E−02 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.0002 1 ms Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.05 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for source’s geometry ksg 1.004 1 — 04 Certificate NPL 2016030013-1 Correction factor for air density kP,T 1.3035 1 0.003 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for polarity effects kpol 0.9999 1 0.0054 — V1 = +300 V, V2 = −300 V Correction factor for recombination effects krec 1.0003 1 0.006 — V1/2 = +150 V Correction factor for radioactive decay kd 1.0010 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.02899 0.3294 Reference air kerma rate K̇R 2.426E−02 Gy h−1 Combined uncertainty uc 1.46E−04 G h−1 0.6% Expanded uncertainty U(k=2) 2.91E−04 Gy h−1 1.2% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 127.7 Gy C-1 — 0.4 Certificate NPL 2016030013-1 Long-term stability kest 1.00 1 0.17 — Table 4 Average charge measurement with the standard Q̅std −2418.86 ‘nC’a 0.004 — n = 10 Average leak charge Q̅l,std −3.00E−02 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.0002 1 ms Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.05 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for source’s geometry ksg 1.004 1 — 04 Certificate NPL 2016030013-1 Correction factor for air density kP,T 1.3035 1 0.003 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for polarity effects kpol 0.9999 1 0.0054 — V1 = +300 V, V2 = −300 V Correction factor for recombination effects krec 1.0003 1 0.006 — V1/2 = +150 V Correction factor for radioactive decay kd 1.0010 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.02899 0.3294 Reference air kerma rate K̇R 2.426E−02 Gy h−1 Combined uncertainty uc 1.46E−04 G h−1 0.6% Expanded uncertainty U(k=2) 2.91E−04 Gy h−1 1.2% a‘nC’, nominal nC. Table 6a. Uncertainty budget for the calibration of the Microselectron V2 source in terms of K̇R using the secondary standard SI 90008 well chamber serial A963391, measurements realized by the SSDL-ININ at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 127.7 Gy C-1 — 0.4 Certificate NPL 2016030013-1 Long-term stability kest 1.00 1 0.17 — Table 4 Average charge measurement with the standard Q̅std −2418.86 ‘nC’a 0.004 — n = 10 Average leak charge Q̅l,std −3.00E−02 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.0002 1 ms Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.05 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for source’s geometry ksg 1.004 1 — 04 Certificate NPL 2016030013-1 Correction factor for air density kP,T 1.3035 1 0.003 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for polarity effects kpol 0.9999 1 0.0054 — V1 = +300 V, V2 = −300 V Correction factor for recombination effects krec 1.0003 1 0.006 — V1/2 = +150 V Correction factor for radioactive decay kd 1.0010 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.02899 0.3294 Reference air kerma rate K̇R 2.426E−02 Gy h−1 Combined uncertainty uc 1.46E−04 G h−1 0.6% Expanded uncertainty U(k=2) 2.91E−04 Gy h−1 1.2% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Calibration factor NKR 127.7 Gy C-1 — 0.4 Certificate NPL 2016030013-1 Long-term stability kest 1.00 1 0.17 — Table 4 Average charge measurement with the standard Q̅std −2418.86 ‘nC’a 0.004 — n = 10 Average leak charge Q̅l,std −3.00E−02 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.0002 1 ms Electrometer calibration factor kel 0.9988 nC/‘nC’a — 0.05 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for source’s geometry ksg 1.004 1 — 04 Certificate NPL 2016030013-1 Correction factor for air density kP,T 1.3035 1 0.003 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for polarity effects kpol 0.9999 1 0.0054 — V1 = +300 V, V2 = −300 V Correction factor for recombination effects krec 1.0003 1 0.006 — V1/2 = +150 V Correction factor for radioactive decay kd 1.0010 1 0.001 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.02899 0.3294 Reference air kerma rate K̇R 2.426E−02 Gy h−1 Combined uncertainty uc 1.46E−04 G h−1 0.6% Expanded uncertainty U(k=2) 2.91E−04 Gy h−1 1.2% a‘nC’, nominal nC. Table 6b. Uncertainty budget for the calibration coefficient NK̇R for SI A973052 transfer chamber in terms of K̇R using the Microselectron V2 source, measurements made by the SSDL-ININ at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.426E−02 Gy h−1 — 0.6 Table 6a Long-term stability kest 1.00 1 0.15 — Table 4 Average charge measurement with the transfer chamber Q̅std −2410.2 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −4.35E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibración factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3058 1 0.001 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for recombination effects krec 1.0005 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kd 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 0.3690 Calibration coefficient NKR 4.627E+05 Gy A−1 h−1 Combined uncertainty uc 2.92E+03 Gy A−1 h−1 0.63% Expanded uncertainty U(k=2) 5.83E+04 Gy A−1 h−1 1.25% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.426E−02 Gy h−1 — 0.6 Table 6a Long-term stability kest 1.00 1 0.15 — Table 4 Average charge measurement with the transfer chamber Q̅std −2410.2 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −4.35E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibración factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3058 1 0.001 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for recombination effects krec 1.0005 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kd 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 0.3690 Calibration coefficient NKR 4.627E+05 Gy A−1 h−1 Combined uncertainty uc 2.92E+03 Gy A−1 h−1 0.63% Expanded uncertainty U(k=2) 5.83E+04 Gy A−1 h−1 1.25% a‘nC’, nominal nC. Table 6b. Uncertainty budget for the calibration coefficient NK̇R for SI A973052 transfer chamber in terms of K̇R using the Microselectron V2 source, measurements made by the SSDL-ININ at Mexico City altitude. Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.426E−02 Gy h−1 — 0.6 Table 6a Long-term stability kest 1.00 1 0.15 — Table 4 Average charge measurement with the transfer chamber Q̅std −2410.2 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −4.35E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibración factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3058 1 0.001 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for recombination effects krec 1.0005 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kd 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 0.3690 Calibration coefficient NKR 4.627E+05 Gy A−1 h−1 Combined uncertainty uc 2.92E+03 Gy A−1 h−1 0.63% Expanded uncertainty U(k=2) 5.83E+04 Gy A−1 h−1 1.25% Component Symbol Value Unit Uncertainty Remark si×100 ui×100 Reference air kerma rate K̇R 2.426E−02 Gy h−1 — 0.6 Table 6a Long-term stability kest 1.00 1 0.15 — Table 4 Average charge measurement with the transfer chamber Q̅std −2410.2 ‘nC’a 0.002 — n = 10 Average leak charge for the transfer chamber Q̅l,std −4.35E−03 ‘nC’a — — Integration time 60 s Integration time t 60 s — 0.001 Electrometer calibración factor kel 0.9988 nC/‘nC’a — 0.09 SI MAX 4000 s/n F092884 ININ Certificate IF.CB.LME-0434–2015 traceable to CENAM Correction factor for air density kP,T 1.3058 1 0.001 0.05 P = 774.18 ± 0.01 hPa, T = 19.316 ± 0.002°C Correction factor for recombination effects krec 1.0005 1 0.003 — V1 = +300 V, V1/2 = +150 V Correction factor for radioactive decay kd 1.0008 1 0.0010 — Normalized to 2016 08 22, 18:53 central time of Mexico Quadratic sum 0.0225 0.3690 Calibration coefficient NKR 4.627E+05 Gy A−1 h−1 Combined uncertainty uc 2.92E+03 Gy A−1 h−1 0.63% Expanded uncertainty U(k=2) 5.83E+04 Gy A−1 h−1 1.25% a‘nC’, nominal nC. Table 7. Uncertainty budget for the ratio RININ/CPHR. Chamber NKR 105/Gy A−1 h−1 ± uc% ININ ustb% NKR 105/Gy A−1 h−1 ± uc% CPHR RCPHR uc A002423 4.645 ± 0.49% 0.48 4.701 ± 0.46% 0.988 0.008 A941755 5.041 ± 0.49% 0.47 5.099 ± 0.46% 0.989 0.009 A973052 4.627 ± 0.49% 0.56 4.679 ± 0.46% 0.989 0.008 Birge’s average 0.989 0.005 Chamber NKR 105/Gy A−1 h−1 ± uc% ININ ustb% NKR 105/Gy A−1 h−1 ± uc% CPHR RCPHR uc A002423 4.645 ± 0.49% 0.48 4.701 ± 0.46% 0.988 0.008 A941755 5.041 ± 0.49% 0.47 5.099 ± 0.46% 0.989 0.009 A973052 4.627 ± 0.49% 0.56 4.679 ± 0.46% 0.989 0.008 Birge’s average 0.989 0.005 Table 7. Uncertainty budget for the ratio RININ/CPHR. Chamber NKR 105/Gy A−1 h−1 ± uc% ININ ustb% NKR 105/Gy A−1 h−1 ± uc% CPHR RCPHR uc A002423 4.645 ± 0.49% 0.48 4.701 ± 0.46% 0.988 0.008 A941755 5.041 ± 0.49% 0.47 5.099 ± 0.46% 0.989 0.009 A973052 4.627 ± 0.49% 0.56 4.679 ± 0.46% 0.989 0.008 Birge’s average 0.989 0.005 Chamber NKR 105/Gy A−1 h−1 ± uc% ININ ustb% NKR 105/Gy A−1 h−1 ± uc% CPHR RCPHR uc A002423 4.645 ± 0.49% 0.48 4.701 ± 0.46% 0.988 0.008 A941755 5.041 ± 0.49% 0.47 5.099 ± 0.46% 0.989 0.009 A973052 4.627 ± 0.49% 0.56 4.679 ± 0.46% 0.989 0.008 Birge’s average 0.989 0.005 Discussion The calibration coefficients obtained by the ININ and the CPHR are consistent with the experimental uncertainty and are considered satisfactory according to the value of the statistic En ≤ 1(16) (Table 3). However, all values of NK̇R determined by the SSDL-ININ are underestimated by −1.1% with respect to the values determined by the SSDL-CPHR (Table 3 and Figures 3 and 4). A possible explanation for this underestimation is that is due to an overestimation of the value of K̇R by both the SSDL-ININ and the SSDL-CPHR given the atmospheric pressure conditions of 774 hPa when the comparison was made. There are three arguments to consider for this possible cause of variation: The SI 90008 chambers with holders 70009 and 70016 need the use of an additional correction factor for kP,T(24, 25). Indeed, reference(26) for high-energy photons concludes that there is a breakdown in the kP,T factor for medium-sized cavities related to the non-equivalence of air with the chamber walls. In other words, this non-equivalence of air implies that the electronic equilibrium conditions are not met by the secondary electron field in the cavity, and so the application of the kP,T factor is no longer valid, since there is only a partial deposition of kinetic energy by the secondary electrons, the so-called ‘terminators’(24). The following factors further complicate this over-correction problem: The materials and size of the cavity, see Figure 2, which shows a sectioned drawing of the chamber. Backscatter from the aluminum wall of the chamber(24). To show the order and importance of the non-equivalence of the aluminum walls of the SI well chamber with the surrounding air, we calculate the ratio of (μρ̅)Al,air=1.0101 and (μenρ̅)Al,air=1.0860, where the sub-index Al, air means the ratio of the mean value of (μρ), calculated from the spectrum of the Ir 192 MicroSelectron V2 source(27). Indeed, the ratio of the mass coefficients is 1–8.6%, which means a correction in that interval for the most simplified case for the 192Ir spectrum. This correction is better understood if it is compared to the behavior of ionization chambers with air equivalent walls (C552 plastic) in X-ray dosimetry, where in fact there is no breakdown of the kP,T, see Figures 4 and 5 of reference(28) or the figures for the Exradin A2 chamber in reference(29). Therefore, we can conclude on a first approximation from these ratios that the variation in Figure 4(24), which shows the breakdown of the conventional kP,T factor, is due to the non-equivalence of the chamber walls to air. In other words, the electronic equilibrium conditions are not being met for this medium-sized cavity(24, 25); where, strictly, the butyrate should also be considered as part of the wall of the chamber. In agreement with the results of the regional comparison SIM RI (I)-K3 of orthovoltage x-rays for CCRI (I) radiation qualities(30), in general, ININ’s values of NK are underestimated by −1.2% with respect to those determined by the other laboratories located close to sea level. These low NK values are due to the underestimation of the air kerma rate values, when the conventional factor kP,T is applied to the ionization currents measured at ININ’s local air pressure (in the order of 710 hPa). In this comparison, the additional correction factors k′P,T;MC given in references(26, 28) are not applied. ININ reported that the correction factor k′P,T;MC should be applied in addition to kP,T because the SSDL-ININ is located 3000 m above the sea level. Nevertheless, an argument that leads us to think that the main cause of variation of the ratios, is the failure of kP,T. In fact, the results obtained in the SIM-K3 comparison for x-ray orthovoltage are also underestimated(30). These are expressed on the degree of equivalence DININ and its expanded uncertainty U, as −9.0 ± 16.0 mGy/Gy for 100 kV, −12.0 ± 16.0 mGy/Gy for 135 kV, −11.1 ± 16.1 mGy/Gy for 180 kV and −12.0 ± 16.1 mGy/Gy for 250 kV. The SSDL-ININ has two ionization chambers: the NE2611 s/n 176 and the Exradin A12 s/n 71931, both calibrated in terms of Dw and Ka for 60Co, at the RI section of the BIPM. The calibration certificate indicates that in the case of the NE2611 chamber (graphite walls) the ionization currents measured at air pressures in the order of 700 hPa, even when corrected by the conventional factor kP,T are underestimated by −0.2% (−2 parts per 1000 or −2 mGy/Gy) with respect to the measured current at normal pressure conditions (103.25 hPa) for 60Co energy. However, this effect is not observed for the Exradin A12 chamber whose walls are made of plastic C552(31, 32). On the other hand, in addition to the influence of the failure of the correction factor kP,T, there are other sources of variation that affect the values of the RININ/CPHR ratios, such as(33): The different traceability of the laboratories, as can be seen from the reference(34). However, as shown in Table 10, the values of the degree of equivalence Dij of +0.3 mG/Gy for the PTB and −1.1 mGy/Gy for the NPL are not enough to explain the variations in the order of 1% of the values of the calibration coefficients The use of different types of sources in the calibration of secondary standards and transfer chambers. Particularly, the PTB and this comparison used the same type of source but different to that used in the NPL (Table 1). Although, the NPL applies a correction factor for the source geometry ksg that corrects this variation(12, 35), which decreases the uncertainty in the determination of K̇R and the calibration factors determined by the ININ. The variation in the determination of the maximum response point (sweet spot), according to the analysis of the response curves implies a variation of 0.05–0.07%, which is not a significant cause explaining the variation of 1%. The contribution of the room scattering is kept to almost zero as each well chamber remained in the same position, at least 1 m from the walls, floor and ceiling during the course of the comparison(36). Figure 2. View largeDownload slide Schematic diagram of the SI HDR 1000 Plus chamber, showing the source holder volume, air-filled active volumes, collecting electrode and Al walls. Figure 2. View largeDownload slide Schematic diagram of the SI HDR 1000 Plus chamber, showing the source holder volume, air-filled active volumes, collecting electrode and Al walls. Additionally, to complete and demonstrate the validity of the later analysis, two means test sets are performed for the K̇R and NKR values, respectively(22): One-way ANOVA test (Tukey method) and one-way ANOM test of mean values for K̇R, α = 0.05%: H0:K̇R,CPHR=K̇R,ININ (6a) Therefore, according to the results of Table 8a and Figure 3, we reject H0 and conclude that the K̇R mean values determined by each laboratory are statistically significant, i.e. there is a cause of variation for this difference that should be investigated further. One-way ANOVA test (Tukey method) and one-way ANOM test for mean values of NKR: H0:NKR,CPHR=NKR,ININ (6b) Table 8a. One-way ANOVA: K̇R versus SSDL. Source DF SS MS F P SSDL 1 0.2647076 0.2647076 11973.37 0.000 Error 13 0.0002874 0.0000221 Total 14 0.2649950 Source DF SS MS F P SSDL 1 0.2647076 0.2647076 11973.37 0.000 Error 13 0.0002874 0.0000221 Total 14 0.2649950 Table 8a. One-way ANOVA: K̇R versus SSDL. Source DF SS MS F P SSDL 1 0.2647076 0.2647076 11973.37 0.000 Error 13 0.0002874 0.0000221 Total 14 0.2649950 Source DF SS MS F P SSDL 1 0.2647076 0.2647076 11973.37 0.000 Error 13 0.0002874 0.0000221 Total 14 0.2649950 Figure 3. View largeDownload slide Graph for the one-way ANOM test for the K̇R values by SSDL obtained in this comparison. Figure 3. View largeDownload slide Graph for the one-way ANOM test for the K̇R values by SSDL obtained in this comparison. Therefore, according to the results of Table 8b and Figure 4, we accept H0 and conclude that the mean values as determined by each laboratory are statistically equal. Table 8b. One-way ANOVA: NKR versus SSDL. Source DF SS MS F P SSDL 1 239625631 239625631 0.60 0.444 Error 28 11113892171 396924720 Total 29 11353517802 Source DF SS MS F P SSDL 1 239625631 239625631 0.60 0.444 Error 28 11113892171 396924720 Total 29 11353517802 Table 8b. One-way ANOVA: NKR versus SSDL. Source DF SS MS F P SSDL 1 239625631 239625631 0.60 0.444 Error 28 11113892171 396924720 Total 29 11353517802 Source DF SS MS F P SSDL 1 239625631 239625631 0.60 0.444 Error 28 11113892171 396924720 Total 29 11353517802 Figure 4. View largeDownload slide Graph for the one-way ANOM test for NKR by each SSDL obtained in this comparison. Figure 4. View largeDownload slide Graph for the one-way ANOM test for NKR by each SSDL obtained in this comparison. Therefore, although the values of K̇R are statistically different, the NKR values are statistically equal: how to explain this? Let us make the following heuristic analysis, aided by the following hypotheses: If the measurements with the HDR 1000 Plus and holder 70010 have the same overestimation as the measurements of the ionization currents made with holder 70009, (for the HDR 192Ir sources calibrated at 770 hPa this overestimation is 1.004(24)); the application of an additional factor k′P in the order to 0.996 is required. Now from Table 9, the value of k′P for the PTW chamber 3304 with holder H0379 T33002.1.009 is determined, assuming that hypothesis (6a) is valid for the corrected values of K̇R. Therefore, this PTW well chamber overestimates the values of K̇R by 1.6% (16 mGy/Gy), when the ionization currents are measured (at P ≈ 710 hPa) and corrected with the conventional correction factor kP. This deviation due to the overestimation of kP is greater than the one associated with the use of different sources: 3 mGy/Gy as assumed by the CPHR(9); or 4 mGy/Gy determined by the NPL(12, 35). However, in this comparison the former contribution of uncertainty in the case of CPHR does not apply; because, we are using a Microselectron V2 source, the same brand and model that PTB does, to calibrate this chamber (Table 1). However, it is necessary to determine and validate these k′P values and their uncertainties (for all atmospheric pressures), for example, with Monte Carlo techniques for both types of well chambers. Most importantly is to verify that the non-equivalence of the wall material to air is the main physical cause for the overestimation of K̇R. This is associated with the generation of the secondary field of electrons, and how these transport and deposit their energy in the internal and external air cavities of the well chamber(25). All SI chambers’ coefficients NK̇R calculated from the KṘ, determined by CPHR with the secondary standard PTW 3304-0154, are overestimated in 1.1%. This is because the behavior of the SI’s chambers does not cancel out the overresponse of the PTW chamber. However, when the SI chambers are calibrated with the secondary standard SI-9008-A963391, the overestimation effects are canceled between the SI transfer chambers and the SI standard. In fact, the NK̇R value of 4.67E + 05 Gy A−1 h−1 and 4.65E + 05 Gy A−1 h−1 reported by the PTB and the CPHR respectively, for the SI-90008-A973052 chamber calibrated close to sea level, the percentage differences are in the order of 0.4%. ININ’s NKR value obtained on this comparison for the same chamber is 4.63E5 Gy A−1 h−1 (Tables 3 and 6b). Finally, the null hypothesis of the mean test is accepted for NK̇R, because the SI 90008-A941755 chamber has a different sensitivity (lower volume) than the SI 90008-A973052 and A02423 transfer chambers. Therefore, the large variation of the average of the calibration coefficients, in order of 4% hiding the variation of 1% that exists between the determinations of NK̇R, made by the CPHR and the SSDL-ININ (Figure 5). Table 9. Parameters for the heuristic determination of k′P to PTW well chamber model 3304. Factor SSDL Unit CPHR ININ NKR 9.160E+05 4.597E+05 Gy h−1 A−1 I 20.451 40.307 nA kpol 1.0026 0.9999 1 krec 1.0005 1.0003 1 ksg — 1.0004 1 kPT 1.3059 1.3035 1 K̇R,Exp 0.0245 0.0243 Gy h−1 k′P 0.984 0.996 1 K̇R,Corr 0.0242 0.0242 Gy h−1 Factor SSDL Unit CPHR ININ NKR 9.160E+05 4.597E+05 Gy h−1 A−1 I 20.451 40.307 nA kpol 1.0026 0.9999 1 krec 1.0005 1.0003 1 ksg — 1.0004 1 kPT 1.3059 1.3035 1 K̇R,Exp 0.0245 0.0243 Gy h−1 k′P 0.984 0.996 1 K̇R,Corr 0.0242 0.0242 Gy h−1 View Large Table 9. Parameters for the heuristic determination of k′P to PTW well chamber model 3304. Factor SSDL Unit CPHR ININ NKR 9.160E+05 4.597E+05 Gy h−1 A−1 I 20.451 40.307 nA kpol 1.0026 0.9999 1 krec 1.0005 1.0003 1 ksg — 1.0004 1 kPT 1.3059 1.3035 1 K̇R,Exp 0.0245 0.0243 Gy h−1 k′P 0.984 0.996 1 K̇R,Corr 0.0242 0.0242 Gy h−1 Factor SSDL Unit CPHR ININ NKR 9.160E+05 4.597E+05 Gy h−1 A−1 I 20.451 40.307 nA kpol 1.0026 0.9999 1 krec 1.0005 1.0003 1 ksg — 1.0004 1 kPT 1.3059 1.3035 1 K̇R,Exp 0.0245 0.0243 Gy h−1 k′P 0.984 0.996 1 K̇R,Corr 0.0242 0.0242 Gy h−1 View Large Figure 5. View largeDownload slide Average NK̇R values of the transfer chambers of the SSDLs. Figure 5. View largeDownload slide Average NK̇R values of the transfer chambers of the SSDLs. Degree of equivalence Dij according to key comparison BIPM RI (I) K-8 An interesting aspect of this bilateral comparison is to try to link it with the results of the key comparison BIPM RI (I)-K8(7, 34). In particular, reference(37) establishes the relationship between the results of the i-th laboratory and the key comparison reference value (KCRV): Ri=NK,iNK,LINK⋅KLINKKBIPM=KiIi⋅ILINKKLINK⋅KLINKKBIPM, (7a) where the variance for the quotient Ri is given by the following equation: uR,i2=[ui2+uBIPM2−∑nfn2⋅(ui,n2+uBIPM,n2)]+ustab2+uLINK2 (7b) Finally, the degree of equivalence for the i-th laboratory is the difference: Di=Ri−1, (7c) and its expanded uncertainty is defined as follows: Ui=2⋅uR,i (7d) For pair-wise degrees of equivalence, Di,j=Di−Dj (8a) with variance: ui,j2=(ui2+uj2−∑nfn2⋅(ui,n2+uj,n2))+2ustab2 (8b) When using multiple transfer instruments (designated by subscript p), the expression for Ri becomes: Ri=∑pRi,pustab,p2∑p1ustab,p2 (9a) and, 1ustab2=∑p1ustab,p2 (9b) Therefore, in our case, the ratios Ri,j are defined as follows(7, 34, 37): RCPHR/BIPM=RCPHR/PTB⋅RPTB/BIPM, (10a) where: RCPHR/PTB=NCPHRNPTB, (10b) analogously, RININ/BIPM=RININ/NPL⋅RNPL/BIPM, (10c) RININ/NPL=NININNNPL, (10d) Now, the ratio RININ/BIPM/RCHPR/BIPM is calculated as follows: RININ/BIPM=RININ/CPHR⋅RCPHR/BIPM (10f) Then, with the results reported for Ri,j and ui,j in references(7, 9, 10) and generalized equations (8a, 8b, 9a, 9b) for the case of more than one transfer instrument and two link laboratories(37), we have the results of Table 10. Table 10. Degrees of equivalence for the bilateral comparison ININ CPHR. NMI/DIa Rij uij Dij Uij Date/reference mGy/Gy PTB/BIPM 1.0003 0.0099 +0.3 19.8 2011(31) NPL/BIPM 0.9989 0.0057 −1.1 11.4 2010(31) CPHR/PTB 1.0022 0.0035 +2.2 7.0 2014(9) CPHR/BIPM 1.0025 0.0105 +2.5 21.0 ININ/CPHR 0.9885 0.0049 −11.5 9.8 2016 ININ/BIPM 0.9910 0.0116 −9.0 23.2 NMI/DIa Rij uij Dij Uij Date/reference mGy/Gy PTB/BIPM 1.0003 0.0099 +0.3 19.8 2011(31) NPL/BIPM 0.9989 0.0057 −1.1 11.4 2010(31) CPHR/PTB 1.0022 0.0035 +2.2 7.0 2014(9) CPHR/BIPM 1.0025 0.0105 +2.5 21.0 ININ/CPHR 0.9885 0.0049 −11.5 9.8 2016 ININ/BIPM 0.9910 0.0116 −9.0 23.2 aNMI stands for National Metrology Institute and DI for Designated Institute. Table 10. Degrees of equivalence for the bilateral comparison ININ CPHR. NMI/DIa Rij uij Dij Uij Date/reference mGy/Gy PTB/BIPM 1.0003 0.0099 +0.3 19.8 2011(31) NPL/BIPM 0.9989 0.0057 −1.1 11.4 2010(31) CPHR/PTB 1.0022 0.0035 +2.2 7.0 2014(9) CPHR/BIPM 1.0025 0.0105 +2.5 21.0 ININ/CPHR 0.9885 0.0049 −11.5 9.8 2016 ININ/BIPM 0.9910 0.0116 −9.0 23.2 NMI/DIa Rij uij Dij Uij Date/reference mGy/Gy PTB/BIPM 1.0003 0.0099 +0.3 19.8 2011(31) NPL/BIPM 0.9989 0.0057 −1.1 11.4 2010(31) CPHR/PTB 1.0022 0.0035 +2.2 7.0 2014(9) CPHR/BIPM 1.0025 0.0105 +2.5 21.0 ININ/CPHR 0.9885 0.0049 −11.5 9.8 2016 ININ/BIPM 0.9910 0.0116 −9.0 23.2 aNMI stands for National Metrology Institute and DI for Designated Institute. The results shown in this table are preliminary, except those published by the BIPM in reference(34) are definitive and official, meaning our results are tentative and approximate and they must be validated according to the rules of the MRA(6). CONCLUSIONS According to the results obtained in this comparison, see Table 3, the SSDL-ININ has demonstrated its technical competence to determine K̇R, and the calibration of well chambers in the energy of the 192Ir for this quantity, within the declared uncertainty. However, the overestimation of −1.1% in K̇R and NKR values is caused by the breakdown of kPT for SSDL-ININ atmospheric conditions. A failure that as far as our knowledge is concerned is due to the electronic equilibrium conditions not being fulfilled, in our specific case for the medium-sized well chamber cavity, owing to the non-equivalence to air of its walls, according to references(26, 28). In addition, we relate these effects to the results of this bilateral comparison with those of key comparison BIPM RI (I)-K8(34), where we indirectly obtained a preliminary degree of equivalence DCPHR: (+2.5 ± Uij = 21.0) mGy/Gy for the SSDL-CPHR and a DININ: (−9.0 ± Uij = 23.2) mGy/Gy for the SSDL-ININ. Finally, it is concluded that the codes of practice for the determination of K̇R and NK̇R issued by the IAEA and the IPEM are equivalent. However, for the use of commercial well chambers in the North American, Mesoamerican (Mexican) and South American highlands, or locations with reduced atmospheric pressures (above 1000 m above sea level), it is required to either apply an additional correction factor k′PT, or to use secondary standard chambers designed with air equivalent walls, so as to accomplish the electronic equilibrium condition to reduce the breakdown of kP,T. ACKNOWLEDGEMENTS We wish to thank M.Sc. José Tendilla, manager of Nuclear Applications in Health of Instituto Nacional de Investigaciones Nucleares for the funding of project ININ-ME-06-2016 and the facilities provided for the completion of this work. We are grateful to Dr Mata and M.Sc. Omar Hernandez-Oviedo from the Radiotherapy Unit of the Cancer Center at the American British Cowdray Medical Center; and Dr Aida Mota and M.Sc. Miguel Rodríguez at the Radiotherapy Subdirection of the Instituto Nacional de Cancerología, whose invaluable support directly and indirectly contributed in the development of this comparison. Finally, we appreciate the generous comments of the referee who made us notice the implications of the non-equivalence to air of the well chamber walls. REFERENCES 1 https://www.gob.mx/salud/acciones-y-programas/informacion-estadistica (In Spanish, last accessed 2018-03-26). 2 https://www.cancer.org/cancer/cervical-cancer/treating/radiation.html (In Spanish, last accessed 2018-03-26). 3 DeWerd , L. A. , Ibbott , G. S. , Meigooni , A. S. , Mitch , M. G. , Rivard , M. J. , Stump , K. E. , Thomadsen , B. R. and Venselaar , J. L. A dosimetric uncertainty analysis for photon-emitting brachytherapy sources: report of AAPM Task Group No. 138 and GEC-ESTRO . 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A statistical approach to infer the minimum setup distance of a well chamber to the wall or to the floor for 192Ir HDR calibration . Med. Phys. 35 , 2214 – 2217 ( 2008 ). Google Scholar CrossRef Search ADS PubMed 37 Burns , D. T. and Allisy-Roberts , P. J. The evaluation of degrees of equivalence in regional dosimetry comparisons. CCRI (I) 07-04 (BIPM, Paris) ( 2007 ). © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

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Published: Apr 9, 2018

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