Comparison of AAPM Addendum to TG‐51, IAEA TRS‐398, and JSMP 12: Calibration of photon beams in water

Abstract The American Association of Physicists in Medicine (AAPM) Working Group on TG‐51 published an Addendum to the AAPM's TG‐51 protocol (Addendum to TG‐51) in 2014, and the Japan Society of Medical Physics (JSMP) published a new dosimetry protocol JSMP 12 in 2012. In this study, we compared the absorbed dose to water determined at the reference depth for high‐energy photon beams following the recommendations given in AAPM TG‐51 and the Addendum to TG‐51, IAEA TRS‐398, and JSMP 12. This study was performed using measurements with flattened photon beams with nominal energies of 6 and 10 MV. Three widely used ionization chambers with different compositions, Exradin A12, PTW 30013, and IBA FC65‐P, were employed. Fully corrected charge readings obtained for the three chambers according to AAPM TG‐51 and the Addendum to TG‐51, which included the correction for the radiation beam profile (P rp), showed variations of 0.2% and 0.3% at 6 and 10 MV, respectively, from the readings corresponding to IAEA TRS‐398 and JSMP 12. The values for the beam quality conversion factor k Q obtained according to the three protocols agreed within 0.5%; the only exception was a 0.6% difference between the results obtained at 10 MV for Exradin A12 according to IAEA TRS‐398 and AAPM TG‐51 and the Addendum to TG‐51. Consequently, the values for the absorbed dose to water obtained for the three protocols agreed within 0.4%; the only exception was a 0.6% difference between the values obtained at 10 MV for PTW 30013 according to AAPM TG‐51 and the Addendum to TG‐51, and JSMP 12. While the difference in the absorbed dose to water determined by the three protocols depends on the kQ and P rp values, the absorbed dose to water obtained according to the three protocols agrees within the relative uncertainties for the three protocols.


| INTRODUCTION
The incidence and death rates of cancer have recently been increasing worldwide, 1 highlighting the need for effective cancer treatment methods. Radiation therapy is considered an important step for effective cancer treatment. In radiation therapy, a highaccuracy dose is required to be delivered to the patient to achieve a favorable clinical outcome. 2 (IPSM 1990), 6 and DIN 6800-2, 7 are based on the use of an ionization chamber with a 60 Co absorbed dose to water calibration factor, N 60 Co D;w , and a beam quality conversion factor, k Q , for the radiotherapy beam.
These standards for absorbed dose to water can reduce the uncertainty in the dosimetry of radiotherapy beams 5 and can provide a more robust system of primary standards than air-kerma-based standards. Further, since the publication of AAPM TG-51 and IAEA TRS-398, Monte Carlo (MC) simulation methods 8,9 have been developed and accurately benchmarked [10][11][12] for the calculations of detailed chamber geometries. [13][14][15] Moreover, studies in current literature have provided ionization chamber perturbation correction factors [15][16][17] and beam quality conversion factors. 14,15,18 Although the AAPM TG-51 provided k Q factors for only cylindrical chambers, which represented the majority of reference chambers available at the time of publication, more than 30 different designs for ionization chambers have recently become available. Therefore, the AAPM Working Group on TG-51 published an AAPM Addendum to TG-51 19 and the Japan Society of Medical Physics (JSMP) published a new protocol for JSMP (JSMP 12). 20 Owing to the new accurate values of the k Q factor provided in the AAPM Addendum to TG-51 19 and JSMP 12, 20 the uncertainties in the absorbed dose to water would be smaller than those in the previous reference dosimetry protocols. However, while AAPM TG-51, 4 IAEA TRS-398, 5 and other protocols have been discussed extensively in literature, [21][22][23][24][25] particularly with respect to the advantages and disadvantages of the recommended photon beam quality indices, [26][27][28][29] the IAEA TRS-398, 5   AAPM TG-51 and Addendum to TG-51, 19 and JSMP 12 20 protocols have not yet been compared. The differences that may exist among these protocols could have important consequences for dosimetric evaluation; therefore, in this study, we compared the absorbed dose to water determined for high-energy photon beams according to AAPM TG-51 and the Addendum to TG-51, JSMP 12, and IAEA TRS-398.

2.A | Materials
Three reference-class cylindrical-type ionization chambers (typically, Farmer-type chambers) were investigated. The characteristics of the chambers are given in Table 1 30 and therefore, they are representative chambers for comparing the three protocols. The absorbed dose to water calibration factor N 60 Co D;w for the three chambers was provided by a Japanese secondary standard dosimetry laboratory (Association for Nuclear Technology in Medicine Japan). The calibration factor N 60 Co D;w and voltage for the Exradin A12, PTW 30013, and FC65-P (IBA Dosimetry GmBH, Schwarzenbruck, Germany) chambers were 4.902 9 10 À2 Gy/nC with a voltage of À299 V, 5.33 9 10 À2 Gy/nC with a voltage of À300 V, and 4.858 9 10 À2 Gy/nC with a voltage of À300 V, respectively. Then, the Exradin A12, PTW 30013, and FC65-P chambers were connected to a SuperMAX electrometer (Standard Imaging, Middleton, WI, USA), a RAMTEC 1000 plus electrometer (Toyo Medic, Tokyo, Japan), and a Keithley 35040 Therapy Dosimeter electrometer (Keithley Instruments Inc., Cleveland, OH, USA), respectively.
All the chambers were loaned by the vendors and other institutions, and had to be returned within a short period of time. Therefore, it was not possible to examine the long-term stability for the three chambers. Alternatively, the stability of the three ion chambers was analyzed using long-term N   than a 0.3%. 19 The three ionization chambers met the minimum requirement of megavoltage photon-beam dosimetry.
Measurements for the absorbed dose to water dosimetry and beam quality were performed using a Siemens Artiste linear accelerator (Siemens AG, Erlangen, Germany) using flattened photon beams with energies of 6 MV and 10 MV. Because a modern linear accelerator was used, the short-term repeatability of the linear accelerator when delivering a series of fixed monitor-unit runs was assumed to be less than 0.05%. 19,31 Dosimetry for the absorbed dose to water and measurements of beam quality were performed using a WP1D water phantom (IBA Dosimetry, Schwarzenbruck, Germany). Given the uncertainties in setting the origin for the water phantom software and the movement distance of the chambers from the origin to the reference depth of 10 cm, the uncertainty in the positioning of the chamber at the reference depth (coverage factor k = 1) was estimated at approximately 0.4 mm.   Tables 2 and 3, respectively. Because detailed information about the three protocols can be found in the protocol documents, only the major differences relevant to this study are described below.

2.B | Beam quality for the three protocols
In the following Section 2.C text, we use the notations consistent with the AAPM TG-51 and Addendum to TG-51 protocols. In IAEA TRS-398 and JSMP 12, several notations are comparatively different from those in AAPM TG-51 and the Addendum to TG-51; however, all quantities can essentially be translated to the quantities in the TRS-398 formalisms without loss of meaning. The absorbed dose to water D Q w in a photon beam with beam quality Q is obtained from the following equation.
Where M: fully corrected charge reading from an ionization chamber, Fully corrected charge reading M raw P TP P ion P pol P elec P leak P rp M raw k TP k elec k pol k s M and M Q : fully corrected charge reading; N 60 Co D;w and N D;w; Q0 : absorbed dose to water calibration factor for the 60 Co beam; k Q and k Q; Q0 : beam quality conversion factor; M raw : uncorrected charge reading; P TP and k TP : temperature and pressure correction factor; P ion and k s : correction for incomplete ion collection efficiency; P pol and k pol : correction for any polarity effects; P elec and k elec : correction for the electrometer; P leak : correction for any contribution to the measured reading that is not due to the ionization released by the radiation beam; P rp : correction for considering any off-axis variation in the intensity profile of the radiation field over the sensitive volume of the ionization chamber. k Q : beam quality conversion factor, N 60 Co D;w : absorbed dose to water calibration factor for the 60 Co beam.
M ¼ M raw P TP P ion P pol P elec P leak P rp ; (2) Where M raw : uncorrected charge reading, P TP : temperature and pressure correction factor, P ion : correction for incomplete ion collection efficiency, P pol : correction for any polarity effects, P elec : correction for the electrometer, P leak : correction for any contribution to the measured reading that is not due to the ionization released by the radiation beam, For all three protocols, the reference conditions for measurements of absorbed dose to water included a 100 cm source-surface distance (SSD) or source-axis distance (SAD), 10 9 10 cm 2 field size at a 100 cm SSD or 100 cm SAD, and a 10 cm depth in water with IAEA TRS-398 allowing a 5 cm depth if TPR 20,10 is less than 0.7. For this study, measurements of the absorbed dose to water for the three protocols were performed with an SAD of 100 cm, a depth of 10 cm, and a field size of 10 9 10 cm 2 at the ionization chamber with the angle for the gantry and the collimator set at 0°. Therefore, in this study, the uncorrected charge readings, M raw , at the center of the chamber cavity for all protocols were considered to be the same to reduce the experimental uncertainty in M raw corresponding to an average of at least five readings. The relative humidity was always within 20% to 60% and the humidity correction was not necessary according to the recommendation of the three protocols as long as the relative humidity was in the range of 20% to 80%. 4,5,19,20,32 2.D | Quantification of uncertainties for the three protocols In this study, photon beam calibration was performed only once with each ionization chamber. Because the same set of readings was used to determine the beam calibrations regardless of the protocol applied, the experimental uncertainties, such as the temperature and pressure correction factor, the short-term repeatability of the linear accelerator, setup of field size, SSD/SAD, and chamber depth, were the same for the three protocols. The correction factor for the polarity effect for the three protocols was determined using the same equation.
Similarly, as the same set of readings at each voltage was used to determine the correction for the polarity effects, the uncertainty in the polarity effect of the correction factor was the same for the three protocols. In addition, the same N 60 Co D;w factor was used across the three protocols for a given ionization chamber. The uncertainties in the N 60 Co D;w factor were also the same for the three protocols. In contrast, the user-dependent parts, such as the assignment of the beam quality conversion factor, determination of the correction for incomplete ion collection efficiency, P leak , P rp , and beam quality conversion factor, were performed using different procedures and had different values for the three protocols. In terms of the beam quality conversion factor, the three protocols provided the uncertainty. Therefore, we estimated the uncertainties in the user-dependent parts, namely, the assignment of the beam quality conversion factor, determination of the correction for incomplete ion collection efficiency, P leak , and P rp , according to the ISO Guide to the Expression of Uncertainty in Measurement 33 in order to evaluate the small differences observed among the three protocols.

3.A | Correction factors for charge readings by an ionization chamber for the three protocols
The correction factors for the charge readings obtained for the three ionization chambers using the three protocols are shown in Table 4.
Because the temperature-pressure correction and polarity correction factors for the three protocols were calculated using the same formula, these correction factors had the same values in all three protocols. In addition, because the correction factors for ion collection efficiency by IAEA TRS-398 and JSMP 12 were calculated using the same formula, the correction factors had the same value in these two protocols. The ion collection efficiencies, P ion and k s , as deter-   The fully corrected charge readings for the three ionization chambers obtained according to the three protocols are shown in Table 5

3.B | Beam quality conversion factor for the three protocols
The beam quality conversion factors obtained according to the three protocols are shown in Table 6. These factors obtained according to the three protocols agreed within 0.6%, 0.4%, and 0.3%, for Exradin A12, PTW 30013, and IBA FC65-P, respectively.

3.C | Determining absorbed dose by the three protocols
The absorbed doses to water obtained according to the three protocols are shown in

3.D | Quantification of uncertainties
The ion recombination factors for the three protocols were calculated using a two-voltage method. The relative standard uncertainties (k = 1) in k s for JSMP 12 and IAEA TRS-398 and P ion for AAPM TG-51 were 0.09% and 0.07% at most, respectively. When determining the beam quality conversion factor with the polynomial fits in the Addendum to TG-51, the relative standard uncertainties (k = 1) were 0.05% at the maximum, as with IAEA TRS-398 and JSMP 12.
The leakage currents were measured with all the equipment used in this study, but with no beam. The leakage currents were below the 0.1% level of the chamber reading. Thus, we assumed T A B L E 5 Fully corrected charge readings (nC) from three ionization chambers obtained according to the three protocols. Difference (%) = (Fully corrected charge readings for JSMP 12 or IAEA TRS-398ÀFully corrected charge readings for AAPM TG-51 and Addendum to TG-51)/Fully corrected charge readings for AAPM TG-51 and Addendum to TG-51.
P leak = 1.000 with an associated relative uncertainty (k = 1) of 0.1%. 19 The radiation dose profiles under the reference conditions at a 10 cm depth were determined from a simple 1-D beam profile measurement using a two-dimensional detector array MapCHECK2 (Sun Nuclear Corporation, Melbourne, FL, USA). The P rp factors were calculated from the measured beam profiles. The relative uncertainty for the P rp was assumed to be 0.05% 19 (k = 1).

| DISCUSSION
For the three protocols investigated in this study, a major difference in the fully corrected charge readings, M, was observed due to the variation in P rp , as shown in Table 4. The fully corrected charge readings determined according to AAPM TG-51 and the Addendum to TG-51, which included P rp , were 0.2% and 0.3% higher at 6 MV and 10 MV, respectively, than those determined according to IAEA TRS-398 and JSMP 12. Traditional flattened beams can usually produce uniform beams for a 10 9 10 cm 2 field, and therefore, the P rp value could be close to 1.000. In this study, because of non-uniformities in the beam, the variation in P rp will be a major contributor to the observed discrepancy in M for the three protocols. The same is true for "horns" in a beam profile. 35 The k Q factors for the three protocols were determined by different methods, giving rise to the possibility that different k Q values will be obtained by these methods. The factors for the Addendum to TG-51 were determined using full MC calculations incorporating detailed information about the chamber to better reflect the true chamber geometry. 14,19 In contrast, the result for IAEA TRS-398 was based on a semi-analytic approach that did not consider all details of the chamber geometry. 5 Because the same N 60 Co D;w factor was used across all of the three protocols for a given ionization chamber, the major discrepancy in the absorbed dose to water values obtained for these protocols was due to the difference in the P rp and k Q values. As stated in the previous section, the obtained values of absorbed dose to water for the three protocols agreed within 0.4%, with the exception of a 0.6% difference at 10 MV between AAPM TG-51 and the Addendum to TG-51 and JSMP 12 obtained for PTW 30013, indicating that there is a good agreement within the relative uncertainty for the absorbed dose to water given by the Addendum to TG-51 (Table 2 situation (i) of Ref. 19 ), IAEA TRS-398, and JSMP 12. The P rp may depend on the particular linear accelerator used. Furthermore, the values of the k Q factors should be chamber-specific. This study is concerned with a comparison of the absorbed dose to water as determined for high-energy photon beams according to the three protocols using only the three cylindrical chambers, because of which the potential difference in the absorbed dose to water for the three protocols using a wide range of ionization chambers and linear accelerators remains unknown. Future work is necessary for the comparison of the absorbed dose to water as determined for high-energy photon beams according to the three protocols using a wide range of ionization chambers and linear accelerators.

| CONCLUSION
The absorbed dose to water for the three protocols using the three ionization chambers showed good agreement within the relative uncertainty in the absorbed dose to water given by the three protocols. Because of the use of cylindrical ionization chambers with the same N 60 Co D;w , the major discrepancy between the obtained values of the absorbed dose to water for the three protocols occurred due to the difference in the P rp and the k Q values. The P rp and the k Q values may depend on the linear accelerator and cylindrical ionization chamber used, respectively. Thus, the absorbed dose to water determined for high-energy photon beams according to the three protocols would change depending on the linear accelerator and the cylindrical ionization chamber used in the experiment.

CONFLI CT OF INTEREST
The authors declare no conflict of interest.