Analysis of different protocols using an Exradin A12 cylindrical chamber for electron beam reference dosimetry

The Technical Report Series 398 (TRS-398), Electron Dosimetry Working Party (EWDP), and Task Group 51 (TG 51) are the most important protocols for reference dosimetry. In the case of electron beam reference dosimetry, these protocols recommend using parallel-plate ionization chambers for beams with R 50 values below specific thresholds. However, recent papers suggested using cylindrical chambers for reference dosimetry of all electron beam energies. Here we compared different protocols using a cylindrical chamber with the recommendations of using a parallel-plate chamber and the TRS-398 formalism for the dosimetry of several electron beam energies. We employed electron beams with nominal energies of 4, 6, 9, 12, and 15 MeV of a Varian 2100C linear accelerator, an Exradin A12


INTRODUCTION
The protocols for electron beam reference dosimetry, such as Technical Report Series 398 (TRS-398) [1], Task Group 51 (TG 51) [2], and the Electron Dosimetry Working Party (EDWP) [3], were published in nearly two decades ago. Still, these are considered the standard protocols for reference dosimetry and are employed in most radiotherapy departments worldwide.
The standard protocols recommend using parallel-plate ionization chambers for low-energy electron beam reference dosimetry. TRS-398 and EDWP recommend that the parallel-plate chambers must be used for electron beams with half-value depth in water ( 50the depth of water in which the electron beam deposited 50% of its energy) ≤ 4 −2 , where their use is preferred in higherenergy beams [1,3]. TG 51, in its turn, recommends nearly the same, with the mandatory use of parallel-plate chambers for electron beam energies with 50 ≤ 2.6 −2 [2]. The main reason for these recommendations is related to early publications that reported significant fluence corrections for cylindrical chambers [4]. These significant fluence corrections would result in considerable uncertainties due to cavity size variations between chambers of the same model (due to the manufacturing process) if general correction factors were employed [5]. Also, it was believed that a well-guarded parallel-plate chamber could minimize the effect of the in-scatter electrons perturbation on the measurements [6]; and the thin front windows of these chambers would allow neglecting the wall influence on the measurements [5].
Although the standard protocols presented reliable results over the last two decades, some issues related to their methodologies and assumptions were addressed in more recent publications.
According to the new data reported by Muir and McEwen, the uncertainties associated with the use of cylindrical chambers (NE2571) for all electron beam energies are not worse than for the parallelplate chambers (NACP-02 and Roos) [5]. A Monte Carlo (MC) simulation study showed that the effects of the in-scatter electron perturbation are present in parallel-plate chambers, even for those with wider guard electrodes [5,7]. Another study using MC simulations showed significant influences of the parallel-plate chamber's wall in the reference depth (1.7%), which increased beyond the reference depth [8]. Moreover, some authors have questioned the long-term calibration stability of parallel-plate chambers, recommending their cross-calibration each time they are used [9,10], and stated that using cylindrical chambers would improve the accuracy of the electron beam calibration procedure and make it simpler [5].
In this way, there is still interest in using Farmer-like cylindrical chambers for the reference dosimetry of all electron beam energies. Indeed, some authors suggest that the standard protocols need to be updated in several ways, one of which is to include the use of cylindrical chambers for dosimetry of all electron beam energies [11]. Using cylindrical chambers for the reference dosimetry of all electron beams would simplify the measurements and make it faster since it would be unnecessary to cross-calibrate the parallel plate against the cylindrical reference chamber nor change the chamber type between photons and electron beam measurements.
We aim to compare different electron beam dosimetry protocols using parallel-plate Exradin P11 and cylindrical Exradin A12 chambers. Other studies employed different ionization chambers and focused on the beam quality correction factors [9,10], fluence corrections, chamber-to-chamber variations [5], and new formalisms [11]. Here we aim to quantify how much the results obtained using cylindrical chambers associated with different protocols differ from the standard reference protocol (TRS-398 formalism and parallel-plate ionization chambers). The results shown here can bring confidence in using cylindrical chambers for the dosimetry of all electron beam energies if a parallelplate ionization chamber is unavailable or if the standard protocols are updated to include the use of cylindrical chamber for low-energy electron beams (namely, beams with 50 ≤ 2.6 −2 for the TRS-398 protocol, and with 50 ≤ 4 −2 for the TG 51 protocol) dosimetry.

MATERIALS AND METHODS
We studied the differences between electron beam dosimetry protocols using a parallel plate and cylindrical chambers in this work. We utilized a medical linear accelerator (LINAC) Varian model depth measurement, as recommended by the standard protocols methodologies [1,2]. Following this, we proceed to the dosimetry measurements with the P11 parallel plate and A12 cylindrical ionization chambers. When using the P11, the chamber was positioned at the zref, discounting its front wall (i.e., initially, the chamber emerged 1 mm from the SSD = 100 cm) [1,2]. When using the A12, the measurements were performed with the chamber's central axis positioned at the zref and at the zref + 0.5rcav (where rcav is the internal radius of the chamber's cavity [mm]), to include all evaluated protocols specifications [1,2,11]. All the measurements were carried out using SSD = 100 cm, 100 UM, and the electron beam applicator and frame of 15 x 15 cm 2 , as described before.
Moreover, we measured and applied the correction factors for the effect of a change in polarity applied to the chamber (kpol), lack of complete charge collection (ks), electrometer calibration factor (kelec), and differences of temperature and pressure between the standard laboratory and our facility at the time of the measurements (kTP) to the charge values obtained. Each measurement was performed three times in the same day, and we employed the mean value for the analysis (n = 3).
We repeated this measurement procedure four times along four months (n = 4), varying the operating medical physicist (n = 3).
After collecting the values, we applied different formalisms (evaluated protocols) for the determination of the absorbed dose rate to water (Dw,Q) at the depth of maximum dose (zmax) for each electron beam quality (Q), as described in the following sections.

TRS-398 formalism (standard and adapted)
Here we employed the TRS-398 protocol using a parallel-plate P11 chamber (TRS-398 (pp)) as the reference protocol. Thus, the values of absorbed dose to water determined by the TRS-398 (pp) For the standard TRS-398 protocol, we cross-calibrated the P11 chamber against the A12 using the higher energy electron beam (15 MeV -R50 = 6.42 g.cm -2 ). The cross-calibration procedure was carried out following the protocol recommendations [1]. Briefly, we positioned the center of the A12 chamber at zref + 0.5rcav for the 15 MeV beam and measured the correction factors and the collection charge. After that, we positioned the P11 chamber at zref discounting 1 mm of the front wall (as described before) and measured the correction factors and collection charge. We applied the equations presented in the protocol (for more information, please see chapter 7, section 7.6 of the ref. [1]) and were able to determine the calibration factor in terms of absorbed dose to water (ND,w,Qcross) for the P11 chamber. With this value, we calculated the Dw,Q [Gy] at zmax for each electron beam, using equation 1: Where MQ is the measured charge [C], ND,w,Qcross is the calibration factor [Gy/C] for the P11 chamber obtained from the cross-calibration procedure, and kQ,Q0 is the quality conversion factor [dimensionless] for the P11 chamber obtained by the equation 2: , Where kQ,Qint is the P11 quality conversion factor for the measured beam energy [dimensionless], and kQ0,Qint is the quality conversion factor for the 15 MeV beam. Both values were obtained using a linear interpolation of the values made available by the protocol (Table 7.IV of the ref. [1]).
As one of our objectives, we also employed the A12 cylindrical chamber to obtain the Dw,Q. Since the protocol does not present the kQ,Q0 values for cylindrical chambers for R50<4 g.cm -2 , we employed , 0 ( ) = −0.0027 50 + 0.9306 (3) The second was to employ a power fitting function to the available values since previous data suggests that the curve profile is better represented by a power function [9]. This approach gave us equation 4: , 0 ( ) = 0.9613 50 −0.028 (4) Using these two strategies, we calculated the Dw,Q at zmax, using equation 5: ND,w,Q0 is the calibration factor for the A12 chamber obtained from direct calibration in 60 Co beam by the Calibration Laboratory of the Nuclear and Energy Research Institute (IPEN -São Paulo, Brazil).

TG 51 formalism
Although the TG 51 protocol does not recommend employing a cylindrical chamber for electron beam dosimetry when R50 < 2.6 g.cm -2 , it made available the equations to obtain the quality conversion factors for all energies of electron beams [2]. In this case, the quality conversion factor is In the TG 51 protocol, the chamber is positioned with its central axis at zref, and the protocol also recommends using a gradient correction factor (Pgr [dimensionless]), which can be obtained using equation 7:

Muir 2020 formalism
In 2020, Muir proposed a new formalism for electron beam reference dosimetry based on MC simulations [11]. Here, the quality conversion factor is also factored in two: k'Q and kQ,ecal

Analysis of k Q values for the A12 cylindrical chamber
Using the values of dose obtained by each protocol and employing the equations 3, 4, 5, 8, and 9, we were able to calculate the ideal kQ values so that Dw,Q(eval)/Dw,Q(ref)=1 (i.e., the kQ values that would make the results of each studied protocol equal the TRS-398 results). In this analysis, our kQ notation represents a conversion factor that includes every conversion factor term described by each protocol. Therefore, for the TRS-398 (linear) and (power) approaches the kQ notation represents the ideal kQ,Q0 values, while for the TG 51 it is the product of kecal and k'R50, and for the Muir's formalism, it is the product of kQ,ecal and k'Q. The calculated kQ values (kQ(calc)) were compared with the kQ values provided by the protocols (kQ(prov)).

Analysis and statistics
The results are expressed as the ratio of the absorbed dose rate to water obtained from the evaluated protocols (Dw,Q(eval)) by the absorbed dose rate to water obtained from the reference protocol (Dw,Q(ref)). In the case of the kQ analysis (item 2.4), we also presented the results as the ratio between the conversion factors calculated by those provided by each protocol (kQ(calc)/kQ(prov)).
The data are also discussed in terms of relative percentage differences (equation 11): ( ) 100 (11) The repeated data are presented in the graphs as a mean ± standard deviation of the measurements carried out over four months (n=4) and by different medical physicists (n=3).

RESULTS AND DISCUSSION
We determined the R50, zref, and PDD values at zref values from the PDD curves obtained. These values are presented in Table 1. The values presented in Table 1 were determined using the TRS-398 formalism [1]. The data showed a good agreement with the last LINAC commissioning data available in the department (2011), where the values differed less than 0.05 g.cm -2 from the commissioning data (data not shown).
This agreement shows the reliability of both the LINAC and the ionization chamber.   (pp) showed the biggest ratio values for the low-energy electron beams. When using cylindrical chambers for beams with R50 ≥ 4 g.cm -2 , the protocol recommends linear interpolating kQ,Q0 data to determine the values for a specific R50 value [1]. However, this approach was expected to show the worst results for beams with R50 < 4 g.cm -2 , mainly because the profile of the kQ,Q0 tends to a power function rather than a linear function (especially in low energy beams) [9]. Still, we evaluated this approach because of its convenient simplicity and quickness in the case of the unavailability of a parallel-plate chamber in a department that follows the TRS-398 formalism. In this way, if a linear approach is employed to estimate the kQ,Q0 values from the TRS-398 data, our results show an expected mean difference of around 5.5% from the standard methodology for the 4 MeV beam (R50 of 1.23 g.cm -2 ). When using a power fitting function (TRS-398(power)), the ratios dramatically decrease, reaching lower differences than other protocols for most energies. These results show that in the case of the unavailability of a parallel-plate chamber, one can get acceptable differences (less than 3% [12]) for low-energy electron beams using a power fitting function to determine the kQ,Q0 values from the TRS-398 data.
The results for the 4 MeV beam using the TG 51 protocols showed mean differences of 4 and 3.3% for the TG 51a (kecal from TG 51), and TG 51b (kecal from ref. [9]), respectively. It is worth pointing out that when using the more recent kecal value, obtained by Muir and Rogers using MC simulations (TG 51b), the differences are lower than when using the TG 51 data (TG 51a), which can be related to the systematic uncertainties in the data presented by the TG 51 protocol [9]. Still, when using both TG 51a and b, the values differ more than the power fitting function. Although the comparisons made here are based on different types of chambers (TG 51: cylindrical; TRS-398: parallel-plate), both TG 51 and TRS-398 are from the same era, and their data were obtained employing similar techniques and methodologies, that is, the differences found may be related to uncertainties from both protocols and both chamber types.
Evaluating the Muir, 2020 protocol, we found mean differences of 2.7 and 1.8% for the 4 MeV (R50 of 1.23 g.cm -2 ) and 6 MeV (R50 of 2.33 g.cm -2 ) beams respectively [11]. As the power fitting approach, these data are in the acceptable differences range. Furthermore, this is the most recent protocol, where its data were obtained using more recent and sophisticated methods. Compared with the TG 51 procedure, Muir's protocol claims not to need Pgr correction factor, which would simplify the process and make it more straightforward.
Here, we employed the parallel plate chamber (discounting its front wall -1.0 mm) for the PDD measurements, which is equivalent to use a cylindrical chamber with a shift of 0.5rcav (1.53 mm -A12), as described in the TRS-398 and TG 51 protocols. We employed this methodology for all protocols with the purpose of standardization of the measurements procedure and R50 determination.
However, it is important to mention that Muir's protocol suggests that the effective point of measurement vary with the chamber type. In the case of an Exradin A12 chamber, the Muir's papers suggest using an optimal shift of 0.35rcav (1.07 mm) for the PDD measurements, which is equivalent to a shift of 1.4 mm for the P11 parallel plate chamber. Using these recommended shift values, it would result in slight different values of R50, what may perhaps improve the results found here [9,11].  The ideal values of kQ were calculated (data not shown) to achieve the same dose values as the TRS-398 protocol when employing the other protocols. Thus, it is possible to utilize these values to calculate the absorbed dose to water using the A12 chamber and any of the evaluated protocols, achieving the same values as those of TRS-398. Note that these values were calculated in specific conditions, using a particular ionization chamber and LINAC.
From the Figs. 1 and 2 data, we realized that the differences found were similar to the magnitude of the Pgr values (i.e., MQ (zref+0.5rcav)/MQ (zref)). Therefore, we recalculated the Dw,Q(eval) values using MQ (zref+0.5rcav) instead of MQ (zref), for both the TG 51 and the Muir, 2020 protocols. Fig. 3 shows   When applying the MQ (zref+0.5rcav) values in the Muir, 2020 protocol, we found a difference of 1.2% for the 4 MeV beam and lower values when increasing the beam energy. Moreover, when using the Muir, 2020 protocol, there is no need to use Pgr corrections for dose calculation, making the procedure simpler and faster. In this way, this protocol shows the best cost-benefit profile for electron beam dosimetry (with or without the use of the chamber shifting), as suggested before [5,9,11].

CONCLUSION
Here we presented the comparison between using a parallel-plate P11 chamber with the TRS-398 formalism and a cylindrical A12 chamber using different protocols for electron beam dosimetry. In our case, we present data regarding using an A12 ionization chamber with both wall and electrode made of C-552. Previous studies already commented on their use but showed data only about a chamber with a wall made of graphite and electrodes made of aluminum (NE2571) [5]. Some evaluated protocols showed differences below 3% compared to the TRS-398 (pp) protocol, whereas the Muir, B.R. 2020 protocol showed the best cost-benefit relationship. Therefore, our data can bring confidence in using a cylindrical chamber in the case of unavailability of a parallel-plate chamber or in the case of new protocols implementation (and addendums to the former protocols) that allow the use of cylindrical chamber for electron beam reference dosimetry.
Once again, it is of paramount importance to highlight that the TRS-398 data, and the use of parallel-plate ionization chambers, present some intrinsic uncertainties [5,9,11], which may have