Comparison of detector performance in small 6 MV and 6 MV FFF beams using a Versa HD accelerator

1. Background & purpose Investigate the applicability of a series of detectors in small field dosimetry and the possible differences between their responses to FF and FFF beams. This work extends upon the series of detectors used by other authors to also include metal-oxide-semiconductor field-effect transistors (MOSFETs) detectors and radiochromic film. We also included a later correction of output factors (OFs) recommended by the recently published IAEA´s code of practice TRS 483 on dosimetry of small static fields used in external beam radiotherapy. 2. Materials & methods The OFs, profiles, and PDDs of 6 MV and 6 MV FFF beams were measured with 11 different detectors using field sizes between 0.6 × 0.6 cm2 and 10 × 10 cm2. 3. Results The OFs of the FFF beams were lower than those of the FF beams for field sizes larger than 3 × 3 cm2 but higher for field sizes smaller than 3 × 3 cm2. After applying the IAEA´s TRS 483 corrections, the final OFs were compatible with our initial results when considering uncertainties involved. Small-volume detectors are preferable for measuring the penumbra of these small fields where this attribute is higher in the crossline direction than in the inline direction. The R100 of equivalent-quality FFF beams was higher compared to the corresponding flattened beams. 4. Conclusions We observed no difference for the dose responses between 6 MV and 6 MV FFF beams for any of the detectors. OF results, profiles and PDDs were clearly consistent with the previously published literature regarding the Versa HD linac. Correcting our first OFs, taken as ratio of detector charges, with the IAEA´s TRS 483 corrections to obtain the final OFs, did not make the former significantly different.


Introduction
With technological advances there has been an increase in the use of techniques such as static and dynamic intensity-modulated radiotherapy, volumetric modulated arc therapy, and stereotactic cranial and extra-cranial radiotherapy, as well as the use of flattening filter-free (FFF) beams [1][2][3]. These techniques have the common characteristic of using fields and small segments to maximally optimise patient treatments by varying the fluence without requiring homogeneous flat beams.
Recent studies based on measurements [4][5][6] and Monte Carlo simulations [7,8] for Elekta linacs [9][10][11][12] show the characteristics and advantages of FFF beams over flattening filter (FF) beams, including the highest dose rates, reduced head scattering, less leakage, and smaller outof-field doses, among others. Thus, non-standard FFF beams with small fields have become the object of interest and study.
Small fields are characterised by loss of lateral charged-particle equilibrium [13][14][15][16][17][18]. Moreover, the perturbation correction factors for these particles are difficult to calculate [15]. This results in deviations from Bragg-Gray cavity theory and a lack of balance in the detectors because these have a finite size. Some authors separate these perturbation factors into those caused by volume effects and those due to the difference between the density of the detector and water [19][20][21].
Numerous authors have evaluated these perturbation factors for diodes, diamond detectors, and ionisation chambers (ICs) for small fields using the Monte Carlo method [21][22][23][24][25][26][27]. There are also numerous experimental studies on the response of these detectors [13,14,18,21,28,29], but few of these include FFF beams because they are more commonly used for CyberKnife applications [22,28,30]. The International Atomic Energy Agency (IAEA) code of practice TRS 483, published at the end of 2017 by the time we were preparing this manuscript, collects all these perturbation factors [18].
This study aimed to investigate the applicability of a series of detectors in small field dosimetry and the possible differences between their responses to FF and FFF beams in order to increase the data available to users regarding their characterisation. In this regard, readers should consider the diverse range of equipment used by medical physics services: although these are limited, staff managing them may need additional references to compare their measurements.
In the case of output factors (OFs), we have extended the range of detectors used to include metal-oxide-semiconductor field-effect transistors (MOSFETs) and radiochromic film. First, in the absence of a clear consensus regarding small field OF determination, they were obtained directly as a ratio of detector charge readouts, also considering a daisy-chaining approach [31]. However, with the publication of the corrections recommended by IAEA's code of practice TRS 483 to derive output factors as quotients of absorbed doses [18], we have been able to investigate the agreement between both sets of data. It should not be overlooked that the selection of data among these kinds of sets as an input for planning therapy systems has been posing a critical decision for medical physicists involved in clinical calculations.
HD accelerator are described elsewhere [32][33][34][35]. The beam quality for the 6 MV beam is a tissue phantom ratio (TPR) 20/10 of 0.684 and the TPR 20/10 for the 6 MV FFF beam is 0.674. The accelerator was calibrated to administer 1 cGy/MU at a 10-cm depth in water, for a 10 × 10 cm 2 field, and at a source-to-surface distance of 90 cm.
The OFs were measured with 9 different detectors for field sizes between 0.6 × 0.6 cm 2 and 10 × 10 cm 2 at a 10-cm depth on the PTW BeamScan water phantom (PTW, Freiburg, Germany) under isocentric conditions (source-to-surface distance = 90 cm) and with the DOSE 1 electrometer (IBA Dosimetry, Germany). The TRUFIX system from PTW was used to place the microDiamond detector and the diodes at their effective points with the axis of symmetry parallel to the radiation beam. The ICs were also placed using the TRUFIX system at their geometric centres with their axes of symmetry perpendicular to the radiation beam and parallel to the movement of the leaves. The microMOSFETs and radiochromic films were centred (visually) in the luminous field and perpendicular to the radiation beam following the TRS 483 recommendations [18].
OFs were measured with radiochromic film by placing pieces of the film between blocks of plastic water (CIRS, Norfolk, VA, USA) at a depth of 10 cm. They were then scanned, processed, and analysed with the web application for radiochromic film dosimetry found at http:// www.Radiochromic.com (Radiochromic S.L., Girona, Spain). The OFs were calculated as the average of five 200 MU measurements, corrected for the pressure and temperature for each IC. The measurements presented were normalised to 3 × 3 cm 2 of the OF (the smallest field in which the lateral charged-particle equilibrium was sufficient for both energies).
A 'reference detector'-the average of the most suitable detectors for each field size-was considered for each field size. This was obtained by comparing our results with the available literature published on the different detectors and with the recommendations for use provided the ratio of detector readings in water (corrected for influence quantities) in the clinical field fclin with beam quality Qclin and in the machine specific reference field fmsr with beam quality Qmsr. It should be noted here that TRS 483 uses the symbol Ω f clin ;f msr Q clin ;Q msr instead of OF f clin ;f msr Q clin ;Q msr ; but we keep this last because it is more familiar to the readership. Our OFs are presented in this case normalized to 10 x 10 cm 2 in order to apply the correction factors of TRS 483, for field sizes between 0.6 × 0.6 cm 2 and 4 × 4 cm 2 at a 10-cm depth too.
Along with OFs, we present the experimental uncertainty associated to the ratio of detector readings and also its combination to the uncertainty given in Table 37 of TRS 483 for k f clin ;f msr Q clin ;Q msr to get the uncertainty for OFs.
Moreover, the most critical field OFs (0.6 × 0.6 cm 2 and 1 × 1 cm 2 ) were also studied by means of daisy chaining [36] in 2 x 2 cm 2 , 3 x 3 cm 2 , and 4 x 4 cm 2 . In this situation OFs are obtained as: where int denotes the intermediate square field used for daisy chaining. For the profiles and PDDs, we used the PTW TRUFIX system, placing the ICs parallel to the radiation beam for the profiles and in the perpendicular direction for the PDDs. The detectors and diodes were oriented with the axis parallel to the beam so that their sensitive volume was perpendicular to it, both for the profiles and for the PDDs. Both the crossline and inline profiles, were measured for 6 MV and 6 MV FFF beams and for field sizes between 0.6 × 0.6 cm 2 and 10 × 10 cm 2 at 5 different depths (16,50,100,200, and 300 mm) in the PTW BeamScan water phantom (PTW, Freiburg, Germany) under isocentric conditions (source-to-surface distance = 90 cm) and with the PTW MEPHYSTO mc 2 acquisition system (PTW, Freiburg, Germany). The acquisition mode was continuous with a speed of 2 mm/s and a resolution of 0.5 mm. The field size, penumbra size, flatness, and symmetry were also recorded.
The PDDs were measured with the same equipment and methods as the profiles, from a depth of 30 cm. For the PDDs, the depth of the dose maximum and that of 50% of the absorbed dose (R 100 and R 50 ) values, normalised to the maximum dose distance (d max ) are presented. For the analysis, we used the PTW Analize software (PTW, Freiburg, Germany) for averaging, interpolation, and smoothing of the curves. In the same way as for the OFs, a 'reference detector' was marked for the profiles and PDDs based on our results, previous publications, and recommendations for use, which in our opinion, represents the most appropriate detector for each measurement at each field size.

Outputs factors
The bottom of Tables 2 and 3 show the differences between the detectors with respect to the OF references (shaded entries). As shown by these results, some ICs are not suitable for use with certain field sizes. In other words, where the detector's active volume is the same or a greater order of magnitude than the size of the OF to be measured. For example, the FC65-G camera is not suitable for measuring the OF of 0.6 × 0.6 cm 2 , as shown by its 70% difference with respect to the reference OF. Tables 2 and 3 show that the microMOSFETs and diodes behave properly for all field sizes; the microDiamond detector responded well in fields up to 7 × 7 cm 2 , beyond which it started to underestimate the OF. The PinPoint, Semiflex 3D, CC13-S, and FC65-G ICs underresponded for the smallest fields (0.6 × 0.6 and 1 × 1 cm 2 ) because they have a higher active volume. However, as reported in both Table 2 and 3, these ICs are ideal for dose measurements from larger fields, except for the PinPoint IC which underestimates the OF from 7 × 7 cm 2 because of the central electrode effect.
The reference OFs for each field size correctly correspond with the OFs obtained with the EBT3 radiochromic film, with deviations of less than 3% for both the FF and FFF beams for all The shaded squares highlight the detectors used as a reference for each field size. The bottom of the field sizes. There was no significant difference (less than 3% for all suitable detectors at each field size) in the dose responses between 6 MV and 6MV FFF beams for any of the detectors. As already demonstrated for the Versa HD by other authors [37], the OFs of FFF beams were lower than the FF beams for field sizes larger than 3 × 3 cm 2 , but higher for field sizes smaller than 3 × 3 cm 2 . Finally, in the top of Tables 4 and 5 we show the ratio of detector readings measured directly and also with the daisy chaining in 4 x 4 cm 2 , 3 x 3 cm 2 and 2 x 2 cm 2 along with their corresponding uncertainties. This ratio of detector charges is what was considered as the OF before the TRS 483 publication; nevertheless this code of practice emphasizes that it is not the OF, straightforwardly defined as a quotient of absorbed doses, because the k f clin ;f msr Q clin ;Q msr is mitted or unknown. In the bottom of these tables we present the corrected OFs taking the k f clin ;f msr Q clin ;Q msr from table 26 of TRS 483 along with their uncertainties.
The Tables 4 and 5 show that the uncertainty of the EFD associated with the lack of reproducibility of its reading is about 4 times greater than that of the microDiamond and the SFD for 6 MV, and slightly lower for 6 FFF MV. EFD also had an infra-response for 0.6 x 0.6 cm 2 with both energies.
The process of correcting with TRS 483 k f clin ;f msr Q clin ;Q msr convert dissimilar reading ratios to similar OFs in the case of microDiamond and SFD. Furthermore, final OFs are all compatible with every other when measurement uncertainty is taken into account, for both energies.
The daisy chaining procedure increases the experimental uncertainty by relying on more electrometer readings and seems to result in close reading ratios for microDiamond and SFD, but at the end did not lead to close OFs.
All these results are also shown in a more visual way in Figs 1-8.
The shaded squares highlight the detectors used as a reference for each field size. The bottom of the table shows the difference (expressed as a percentage) between detector responses for each field size with respect to the chosen reference detector. Fig 9 shows the in-plane profiles at a 100-cm depth for the 0.6 × 0.6 cm 2 , 3 × 3 cm 2 , and 5 × 5 cm 2 fields for the 6 MV and 6 MV FFF beams with the Semiflex 3D IC and the microDiamond detector which clearly shows that the penumbra is best characterised by the detector with the  lowest active volume. For the profiles, the values for the field size, penumbra (average of the left and right penumbra), flatness ('unflatness' for the FFF beams), and symmetry for all the field sizes at a 100-mm depth are presented in Tables 6 and 7. The shaded entries in the tables also indicate the reference detector used to make the comparisons and calculate the deviations for each field size. These tables show that the symmetry values for the FF beams are practically equal to those for the FFF beam (within the 100-102.58% range), except for the 0.6 × 0.6 cm 2 field size, for all the detectors. The flatness ('unflatness' for the FFF beams) shows the same behaviour, within the 100-103.18% range for the FF beam and 1.029-1.232% range for the 'unflatness' of the FFF beams.

Profiles
Regarding the penumbra, for both energies and field sizes, the average penumbra in the crossline was greater than in the in-plane at around 1-1.5 mm. The Semiflex 3D IC overestimated both the field size and the penumbra for the smaller field sizes (0.6 × 0.6 cm 2 and 1 × 1 cm 2 ) compared to the other detectors. For the other field sizes (from 2 × 2 cm 2 to 10 × 10  cm 2 ), the field size measurements were within 1% of the difference with respect to each fieldsize reference (shaded entries in Tables 6 and 7), for both the FF and FFF beams. Finally, the Semiflex 3D IC still overestimated the penumbra for these fields size.

Percentage depth dose
As shown in Table 8, some values for the FFF beam are a little higher than for the FF beam, both for R 100 and R 50 . The maximum difference reached was 1.5 mm for R 100 , even though the quality of the FFF beam was matched to be the equivalent of the corresponding flattened beams, as specified in the Elekta customer acceptance test [38].
The shaded entries in the Table 8 show the reference detector used for each field size. For the 0.6 × 0.6 cm 2 and 1 × 1 cm 2 fields the reference detector was the SFD. These measurements were not performed for the PPC40 detector because its volume is greater than these field sizes. The Semiflex 3D detector showed a maximum difference of 15% (less than 2 mm) while the maximum difference of the microDiamond was 4% (less than 0.5 mm) for both the FF and FFF beams.
For 2 × 2 cm 2 fields, in both the FF and FFF beams, the differences for the PinPoint detector were less than 3% (less than 0.5 mm) for the SFD, microDiamond, and Semiflex 3D detectors. For the rest of the field sizes, all the differences between the parameters measured with the different detectors were less than 3%, except for the R 100 which differed by up to 10% (1.5 mm) for the detectors with the lowest active volume (SFD and microDiamond).

Discussion
Firstly, with respect to OFs determination, by the time we were commissioning our 6 MV/6 MV FFF Versa HD, the piece of literature related with this topic was still somewhat heterogeneous. To our knowledge, only Lechner et al. work [27] was sufficiently systematic by covering a wide set of detectors and by reporting a complete series of corrections. This publication was really useful for us to notice detector behaviour and led some of our decisions when providing input for our therapy planning system. However, we decided to use our raw estimates for OFs until an institutional response like an IAEA's code of practice was available. As mentioned before, it has come while preparing this manuscript, so we decided to keep our first determinations, which are representative of what users traditionally did in the absence of calculations of correction factors, and also present the real OFs in the way TRS 483 establishes [18] along with their uncertainties as a basis for a novel comparison.
The major differences between the detector responses is caused by their volumes. Our homogeneous set of measurements showed that MOSFET, microDiamond, and diodes are  Detector comparison for small fields good detectors for small field dosimetry and that these can be complemented with radiochromic film verification, as shown by previously published data [39,40]. For all the detectors analysed, we found the same general trend regardless the type of filtration used.
With the section of our study related to TRS 483 correction factors we have found that applying the k f clin ;f msr Q clin ;Q msr to our measurements makes each set of OFs (microDiamond's and SFD's) compatible with the other. EFD results seem to have a worse behaviour due to the lack of reproducibility of our detector.
Another result derived from our comparison of both sets of data for OFs determination is related with the so-called daisy chaining procedure to ideally minimize OFs error along a broad range of field sizes. This method, initially investigated for mitigating different overresponse of silicon detectors to field size changes by Dieterich and Sherouse [31], has been also addressed by the IAEA's code of practice as mentioned above. However, this procedure does not always bring our ratios of detector readings closer to the true OFs calculated with the TRS 483 corrections. As a consequence, we would discourage other users from relying on daisy chaining and recommend instead use of Eq 1 (see materials and methods section) with IAEA's code of practice factors.  Detector comparison for small fields Table 6. Results of the crossline and inline profile parameters for different detectors at a 100-mm depth depending on the field size for 6 MV beams. 0.6 × 0.6 cm 2 Crossline Inline  Detector comparison for small fields

MV Field size (cm) Penumbra (mm) Flatness (%) Symmetry (%) Field size (cm) Penumbra (mm) Flatness (%) Symmetry (%)
The shaded squares highlight the detectors used as a reference for each field size. Secondly, with regard to profiles acquisitions, the penumbra in the crossline direction (direction of the leaves) was greater than in the jaw direction (inline) for every field size. This difference is caused by higher transmission through the rounded MLC leaves [36]. As seen in our results, high-resolution diodes and small-volume ICs and detectors help to accurately measure the penumbra in these small fields [37,41].
Finally, with respect to percentage depth doses determination, the R 100 of equivalent-quality FFF beams was higher compared to the corresponding flattened beams. This effect was explained by Huang et al., [42] who reported that the R 100 shift was influenced by two competing processes: the increased contribution of low-energy photons caused by removing the flattening filter (upstream R 100 shift), and the increased number of penetrating photons resulting from the increased beam quality (downstream R 100 shift). The combined effect of these two competing processes results in a deeper R 100 for equivalent-quality FFF beams.

Conclusions
There were no substantial differences in the dose responses for FF and FFF beams that could have any clinically relevant consequences for any of the detectors investigated. Both the results of the OF and for the profiles and PDDs are clearly consistent with previously published data relating to the Versa HD, and thus these findings will help other professionals who are commissioning new Versa HD linacs. These data provide valuable insight into accurate beam modelling, which in turn, determines treatment outcomes and patient safety.
Using newly available TRS 483 corrections provide more consistent sets of results for OF determination that daisy chaining procedures. Correcting our first OFs, taken as ratio of detector charges, with the IAEA's TRS 483 corrections to obtain the final OFs, did not make the former significantly different.  The shaded squares highlight the detectors used as a reference for each field size.