The use of 0.5rcav as an effective point of measurement for cylindrical chambers may result in a systematic shift of electron percentage depth doses

Abstract Electron dosimetry can be performed using cylindrical chambers, plane‐parallel chambers, and diode detectors. The finite volume of these detectors results in a displacement effect which is taken into account using an effective point of measurement (EPOM). Dosimetry protocols have recommended a shift of 0.5 rcav for cylindrical chambers; however, various studies have shown that the optimal shift may deviate from this recommended value. This study investigated the effect that the selection of EPOM shift for cylindrical chamber has on percentage depth dose (PDD) curves. Depth dose curves were measured in a water phantom for electron beams with energies ranging from 6 to 18 MeV. The detectors investigated were of three different types: diodes (Diode‐E PTW 60017 and SFD IBA), cylindrical (Semiflex PTW 31010, PinPoint PTW 31015, and A12 Exradin), and parallel plate ionization chambers (Advanced Markus PTW 34045 and Markus PTW 23343). Depth dose curves measured with Diode‐E and Advanced Markus agreed within 0.2 mm at R50 except for 18 MeV and extremely large field size. The PDDs measured with the Semiflex chamber and Exradin A12 were about 1.1 mm (with respect to the Advanced Markus chamber) shallower than those measured with the other detectors using a 0.5 rcav shift. The difference between the PDDs decreased when a Pinpoint chamber, with a smaller cavity radius, was used. Agreement improved at lower energies, with the use of previously published EPOM corrections (0.3 rcav). Therefore, the use of 0.5 rcav as an EPOM may result in a systematic shift of the therapeutic portion of the PDD (distances < R90). Our results suggest that a 0.1 rcav shift is more appropriate for one chamber model (Semiflex PTW 31010).

Cylindrical ionization chambers, a commonly used detector, are recommended by the AAPM TG-25 3 and TG-70 1 protocols. Cylindrical chambers have not been typically recommended for electron energies below 10 MeV. While new works suggests that their use on these small energies may not be incorrect, 4 the use of parallel plate chambers is still recommended for the most part. [ 3,[5][6][7][8] In radiation therapy, the dose to the medium rather than the detector's sensitive volume is required. Since the chamber wall and air cavity displace a volume of the media, which in turn affects the electron fluence in the cavity, the dose to water measured at the reference point of an ionization chamber differs from the dose in the absence of the detector. Thus, it is necessary to apply a correction factor to the raw measurements to account for the detector perturbation. 9,10 The ionization gradient at the point of measurement in an electron beam can be accounted for by applying a gradient correction factor, P gr . The P gr of a cylindrical chamber is a function of the chamber's cavity radius and is unity for a parallel plate chamber. 1 A second method is by positioning the chamber with its geometric center displaced from the point of measurement by an amount that offsets the effect. This point is referred to as the effective point of measurement (EPOM)the depth in the medium where the average energy is the same as in the chamber and is usually a shift from the chamber's reference point. 7 The correct choice of the EPOM is particularly important when measuring depth dose curves. Thus, various studies and protocols have proposed different points within the chamber as the correct EPOM of ionization chambers. [11][12][13][14][15] The International Atomic Energy Agency (IAEA) protocol 5  and 51 recommend a shift of 0.5r cav when using a cylindrical chamber. 1,6 This recommendation was based on studies performed by Johansson et al. 16 and Khan 17 to determine the magnitude of the displacement required to account for the gradient effect. On the other hand, the Institute of Physics and Engineering in Medicine (IPEM) recommends a shift of 0.6r cav . 7 Other independent studies, using both experimental measurements and Monte Carlo based calculations, have been performed to determine the magnitude of the EPOM shift. Indra et al. 12 reported that the EPOM shift is applied in the upstream direction from the central axis of the chamber and it varies from 0.9r cav to 0.5r cav between 6 and 20 MeV beams, respectively. Note that the word upstream will be used in this manuscript to indicate shifts in the direction toward the electron source. Similarly, the word downstream will be used to refer to shifts in the direction away from the electron source. Both upstream and downstream will be used to describe shifts applied to either PDDs or detectors. Legrand et al. 14 experimentally concluded that the corrections recommended in the protocols for cylindrical chambers were not completely appropriate. They suggested applying an EPOM shift equal to 0.87(r cav -1 mm). The experimental work by Huang et al. 13 showed that the use of a constant 0.5 r cav for all electron beams is too simplistic and that this value is expected to approach 0.8 r cav with increasing energy .
Using Monte Carlo simulations, Wang and Rogers 18 recommended a shift of 0.4 r cav -0.5 r cav for depth dose measurement using cylindrical chambers. Work by Voigts-Rhetz et al. 15 showed that the EPOM shift of cylindrical chambers is close to the recommended value of 0.5r cav at higher energies but decreases by over 30% at lower energies.  22 while the SFD is a micro-size sensitive volume detector used in small field dosimetry. 23,24 The SFD is also suitable for electron dosimetry according to the manufacturer. The geometry and physical characteristics of these detectors are listed in Table 2. The reference points of the cylindrical chambers were positioned by eye on the water surface by adjusting its position until its reflection formed a perfect circle. 2 Table 2), were used to investigate the impact of the chamber cavity radius since detectors report averaged dose over their sensitive volume. 29  which has a different EPOM (see Table 2), as a consistency check. The EPOM has also been found from literature data. 20 The diodes were   This shift is also noticeable in the mean values of R 50 of the three detectors obtained for various energies and field sizes as summarized in Table 3. The right axes of Fig. 1   In addition, a non-parametric (Mann-Whitney Wilcoxon) test was performed to check whether the observed differences in the detector readings are statistically significant. The test showed that the difference observed between the Advanced Markus and Diode-E was not significant (P = 1). On the other hand, the differences between the Semiflex and the Advanced Markus were statistically significant (P = 0.01). As expected, the difference between the Semiflex and the Diode-E was also statistically significant (P = 0.01).

3.C | Investigation of the EPOM of the detectors
The selection of the EPOM can result in systematic PDD shifts, and thus, it is necessary to confirm that the appropriate EPOM is used.    in the wall material (differences within by 0.1% and 0.2%, respectively). 32 Therefore, it is likely that the EPOM will be the same for cylindrical chamber with similar design but different wall materials.
The difference between PDDs was reduced with the use of chamber-specific correction factors, for example, using the previously published 0.3r cav 15 for the Semiflex chamber. Figure 5 shows the result of applying an EPOM shift of 0.3r cav (as opposed to 0.5r cav ) to the Semiflex chamber for the 6 MeV and a 10 × 10 cm 2 field size.   15 This observation implies that, with a 0.3r cav shift, the use of a Semiflex chamber results in a more accurate PDD and it is, therefore, an acceptable detector for low energy electron dosimetry.
However, this conclusion is inconsistent with the recommendation of the AAPM TG-51 protocol, which states that the use of well-  Adv. Markus Diode-E Semiflex Exradin Rel_SemiF Rel_AdvM Rel_Exradin F I G . 6. Overlap of percentage depth doses (PDDs) when a 0.1 r cav shift was applied to the Exradin A12 and Semiflex chamber measurements, relative to the PDDs for the Diode-E and Advanced Markus chambers. Relative differences with respect to the diode PDD are also shown (axis on the right side). guarded parallel plate chamber over cylindrical chamber is preferred for low energies (<10 MeV) but not for higher energies.
A numerical analysis of our results suggests that the Semiflex chamber was shifted by a factor of 0.4r cav more than was required. This value was obtained by dividing the 1.1 mm offset observed between the Semiflex and the Advanced Markus by the r cav of the Semiflex. Therefore, it is our finding that applying a 0.1r cav , rather than the recommended 0.5r cav , will result in the depth dose curves of the Semiflex agreeing with those of the Advanced Markus. However, it should be emphasized that this correction is only applicable for this chamber model.
The systematic PDD shifts were quantified using R 50 as a metric.
These PDD shifts were observed by overlapping the curves of different detectors by their appropriate offset. Figure 6 shows the same PDDs of Fig. 1(a) with the exception that the Semiflex curve which has been shifted by 1.1 mm (according to the last column of Table 3).

| CONCLUSION
This study investigated the effect of using different EPOM values to measure electron PDDs with various detectors, particularly cylindrical chambers. It was found that the use of 0.5r cav as an EPOM results in a systematic shift of the therapeutic portion of the PDD (distances < R 90 ). This shift can be as large as 1.1 mm for commonly used cylindrical chambers and decreases with a decrease in cavity size. This shift was observed for all energies and is not only of concern for low energies <10 MeV as suggested by some dosimetry protocols. [3][4][5][6] Our results suggest that an EPOM correction of 0.5r cav is too large and that a 0.1r cav shift gives a better agreement for a specific model (Semiflex PTW 31010).

ACKNOWLEDGMENTS
The authors wish to thank the University of Manitoba and Cancer-Care Manitoba for funding this work. The authors also wish to thank Dong-Chang Lee for his assistance with the measurements and Martin Jensen for translating the German Protocol.

CONFLI CT OF INTEREST
There is no conflict of interest declared in this article.