Validating kQ=1.0 assumption in TG51 with PTW 30013 farmer chamber for Varian TrueBeam's 2.5 MV imaging beam

Abstract AAPM Report 142 recommends and the State of Ohio requires that the imaging dose be quantified in radiotherapy applications. Using the TG51 dose calibration protocol for MV Imaging dose measurement requires knowledge of the kQ parameter for the beam quality and the ionization chamber type under investigation. The %dd(10)x of the Varian TrueBeam 2.5 MV imaging beam falls outside the range of the available data for the calculation of the kQ value. Due to the similarities of the 2.5 MV imaging beam and the 60Co beam, we and others made the assumption that kQ = 1.0 in TG51 calculations. In this study, we used the TG21 and TG51 calibration protocols in conjunction to validate that kQ = 1.0 for the 2.5 MV imaging beam using a PTW 30013 farmer chamber. Standard measurements for TG51 absolute dosimetry QA were performed at 100 cm SSD, 10 cm depth, 10 × 10 field size, delivering 100 Monitor Units to a waterproof Farmer Chamber (PTW TN30013) for both 2.5 and 6 MV. Both the TG21 and TG51 formalisms were used to calculate the dose to water per MU at dmax (Dw/MU) for the 6 MV beam. The calculated outputs were 1.0005 and 1.0004 cGy/MU respectively. The TG21 formalism was then used to calculate (Dw/MU) for the 2.5 MV imaging beam. This value was then used in the TG51 formalism to find kQ for the 2.5 MV imaging beam. A kQ value of 1.00 ± 0.01 was calculated for 2.5 MV using this method.

2.5 MV imaging beam and the 60 Co beam, we and others made the assumption that k Q = 1.0 in TG51 calculations. In this study, we used the TG21 and TG51 calibration protocols in conjunction to validate that k Q = 1.0 for the 2.5 MV imaging beam using a PTW 30013 farmer chamber. Standard measurements for TG51 absolute dosimetry QA were performed at 100 cm SSD, 10 cm depth, 10 9 10 field size, delivering 100 Monitor Units to a waterproof Farmer Chamber (PTW TN30013) for both 2.5 and 6 MV. Both the TG21 and TG51 formalisms were used to calculate the dose to water per MU at d max (D w /MU) for the 6 MV beam. The calculated outputs were 1.0005 and 1.0004 cGy/MU respectively. The TG21 formalism was then used to calculate (D w /MU) for the 2.5 MV imaging beam. This value was then used in the TG51 formalism to find k Q for the 2.5 MV imaging beam. A k Q value of 1.00 AE 0.01 was calculated for 2.5 MV using this method.   and the older Task Group-21 protocols. 4 These two protocols provide methodologies to calculate the dose to water for MV and 60 Co beams. The absorbed-dose-to-water factor, N 60Co D;w , based on the TG51 protocol uses a k Q factor which converts the calibration factor for a 60 Co beam quality, for which the absorbed-dose calibration factor is applicable, to a clinical beam quality of Q. In the TG51 proto- an empirical formula to calculate the k Q for clinical beams of quality with %dd(10) x in the range of 63% to 86% and also provides k Q values for some newer ionization chambers such as PTW TN30013 (PTW GmbH, Freiburg, Germany).
At our institution, we have Varian TrueBeam linear accelerators with 2.5 MV imaging beams. In an effort to meet the requirement of the ODH and to be able to characterize the dose given to patients during imaging with this beam, we set out to perform the dose quantification of the 2.5 MV imaging beam.
In order to have an accurate output measurement, k Q must be known when using the TG51 formalism. We initially performed the calibration of this beam using the TG51 protocol with an assumed k Q value of 1.0. A recently published paper by Gr€ afe et al. 6 showed a similar calibration again with the assumed k Q of 1.0, using the 2.5 MV imaging beam and 0.64 cc Exradin A12 (Standard Imaging Inc., Middleton, WI, USA) ionization chamber.
In order to validate our assumption of k Q = 1.0 for the 2.5 MV imaging beam under consideration with the PTW TN30013 ionization chamber, we performed the calibration of the 2.5 MV with the older TG21 formalism, which does not require any knowledge of k Q . The aim of this study is to use the TG21 protocol for the absolute dosimetry calculation for the 2.5 MV beam to validate the assumed value for k Q to be used in a TG51 protocol absolute dosimetry calibration.
Two previous studies have compared the doses calculated by the TG21 and TG51 protocols for megavoltage beam dosimetry. Cho et al. 7 showed that for PTW N30001 & 23333 ion chambers, the TG51 to TG21 calculated dose ratio was 1.012 and 1.010 for 60 Co and 6 MV photon beams respectively. Tailor et al. 8 calculated the doses using both protocols for a variety of cylindrical chambers and photon beam energies. They showed that for the cylindrical chambers they tested the dose ratios were within AE1.0%, the highest being at the 60 Co beam energy and decreasing with increasing photon energy.

| MATERIALS AND METHODS
We measured the percentage depth dose (PDD) of the 2.5 MV imaging beam of a Varian TrueBeam linear accelerator with a CC13 (IBA Dosimetry, Schwarzenbruck, Germany) detector in a cylindrical 3D Scanner water tank (Sun Nuclear Corporation, Melbourne, FL, USA) for a 10 9 10 cm field size at 100 cm SSD. Our measured %dd(10) x for 2.5 MV is 51.53%. This is shown in Fig. 1. This value is outside the range of %dd(10) x as shown in fig. 4 of the TG51 report or the empirical formula valid range as given in eq. (1) in the TG51 addendum. Measurements were then taken at 10 cm depth, 100 cm SSD, 10 9 10 cm 2 field size with a PTW waterproof farmer chamber (TN30013) to calculate P ion . The exposure calibration factor, N x , and cavity-gas factor, N gas , were taken from the ADCL calibration certificate of the ionization chamber used and were verified against a calculated value of N gas , using eq. (6) in TG21, assuming a PMMA (acrylic) wall and acrylic cap. P wall was calculated using the mass stopping power ratio, L/q, and mean mass energy absorption coefficient, l en /q, listed in the TG21 formalism for the wall material, acrylic, based on specifications from the manufacturer (74% PMMA, 26% graphite). 9 In TG21 protocol, the dose to water is given by The fraction of ionization due to electrons from the chamber wall, a, was taken as zero using Fig. 1  We calculated N gas by using eq. (3) given above and also from N gas ðGy=RÞ ¼ 8:48 Ã 10 À3 N x A ion (4) which is provided on the ADCL calibration certificate and the manufacturer specification sheet [8]. The calculated values of N gas are shown in Table 1.
After calculating (D W /MU) TG21 at the calibration dosimetry conditions using the TG21 protocol, we equated the calculated value to the TG51 equation used to calculate (D W /MU) for the same reference geometry and solved for k Q as shown in eqs. (5) and (6) Numeral values for this calculation are shown in Table 3. As a validation of the method, the same process was applied for the 6 MV beam.

| RESULTS
We calculated the absorbed dose ratio at the reference conditions as (TG51/TG21) Dose = 0.9994 for the 6 MV beam using the PTW 300013 ion chamber. Tailor et al. 8 showed that (TG51/ TG21) Dose = 1.003 for a 6 MV beam using PTW N30006 ion chamber. The N30006 is equivalent to PTW 30013 according to the manufacturer's specifications. 9 Our result differs from Tailor et al.'s prediction by only 0.3%. Hence, we hypothesize that our PTW N30013 chamber material dependent TG21 protocol parameters (L/ q) and (l en /q) are accurate.
Next, by calculating the absorbed dose of the 2.5 MV imaging beam with the TG21 formalism and solving eq. (6), k Q value was calculated as 1.0002 (Table 3).