Evaluation of the IAEA‐TRS 483 protocol for the dosimetry of small fields (square and stereotactic cones) using multiple detectors

Abstract The IAEA TRS 483 protocol1 for the dosimetry of small static fields in radiotherapy was used to calculate output factors for the Elekta Synergy linac at the Australian Radiation Protection and Nuclear Safety Agency (ARPANSA). Small field output factors for both square and circular fields were measured using nine different detectors. The “corrected” output factors (ratio of detector readings multiplied by the appropriate correction factor from the protocol) showed better consistency compared to the “uncorrected” output factors (ratio of detector readings only), with the relative standard deviation decreasing by approximately 1% after the application of the relevant correction factors. Comparisons relative to an arbitrarily chosen PTW 60019 microDiamond detector showed a reduction of maximal variation for the corrected values of approximately 3%. A full uncertainty budget was prepared to analyze the consistency of the output factors. Agreement within uncertainties between all detectors and field sizes was found, except for the 15 mm circular field. The results of this study show that the application of IAEA TRS 4831 when measuring small fields will improve the consistency of small field measurements when using multiple detectors contained within the protocol.


| INTRODUCTION
The release of the first international code of practice for the dosimetry of small static fields IAEA TRS 483 1 was derived by an international working group in collaboration with the American Association of Physicists in Medicine. It aims to deliver worldwide consistency in small field reference dosimetry for clinical radiotherapy, which is traceable to a primary standard. The protocol details the methods and corrections to be applied to various detectors for determining small field output factors, as well as machine specific details.
The protocol was needed due to the increasing clinical use of stereotactic radiotherapy treatments such as Stereotactic Ablative Body Radiotherapy for the targeting of small tumors with single high-dose fractions. [2][3][4][5] The selection of detectors and methods used for the dosimetry of these beams are important for both clinical quality assurance and patient safety during treatment.
Small field dosimetry is challenging, particularly for very small fields due to inherent issues that affect the measured output factors such as steep dose gradients and partial occlusion of the radiation source. 3,6-10 Furthermore, it usually requires a detector with a small active volume and high spatial resolution. 3,8,11 Detector-specific issues including a lack of lateral electronic equilibrium, dose averag-Attempts to consolidate other studies to provide detector correction factors in small fields are difficult due to differences in the how field size was defined, depth and source to surface distances (SSDs) and the size of the reference field. 1 At the time of completing this work there was only one other study, 11 which we were aware of, that had examined the protocol's correction factors for the IBA-SFD detector in circular fields (5-40 mm). A separate study had examined six of the detectors listed in the protocol, 12 and determined large differences between detectors for the uncorrected output factors when using smaller field and cone sizes, with shielded diodes having higher uncertainties due to their construction.
In this work output factors were measured using nine different detectors included in the IAEA TRS 483 protocol. The corrected and uncorrected output factors were compared for five stereotactic cones (nominal 5-50 mm) and seven square fields (1 cm × 1 cm to 6 cm × 6 cm). To investigate the potential variations within detectors of the same type, the output factors of the stereotactic cones were measured using four different PTW 60019 microDiamond detectors. An uncertainty budget was completed for all detectors and relevant field and cone sizes examined.

2.A | Square field measurements
The Elekta Synergy linear accelerator is equipped with a multi-leaf collimator (MLC) consisting of 80 leaves, with a projection of 10 mm at the isocenter. Output factors in field sizes of 1 cm × 1 cm, 1.5 cm × 1.5 cm, 2 cm × 2 cm, 2.5 cm × 2.5 cm, 3 cm × 3 cm, 4 cm × 4 cm and 6 cm × 6 cm (defined by the MLC) were measured, referenced to a 10 cm × 10 cm reference field.

2.B | Stereotactic conical collimator system
The Elekta stereotactic conical collimator system consists of five circular cones of varying diameter, which attach via a plate to the linac head ( Fig. 1).
The output factors in fields defined by circular cones of nominal diameters at the isocenter of 5, 7.5, 10, 15 and 50 mm were measured and referenced to MLC defined 3 cm × 3 cm (for 5-15 mm cones) and 6 cm × 6 cm fields (for the 50 mm cone). The cone axis was aligned to the central axis of the beam and was consistent for all measurements.

2.C | Detectors
Nine different detector types were investigated with their active volumes and description presented in Table 1. The detectors are classed   into one of four categories based on the TRS-483 protocol; unshielded diodes and microDiamond, shielded diodes, micro ionization chambers and mini ionization chambers.

2.D | Measurements
All measurements were completed using the IBA Dosimetry Blue Phantom2 tank with OmniPro-Accept software, scanning volume of 480 mm (l) × 480 mm (w) × 410 mm (h) and positional reproducibility of ±0.1 mm. 13 The output factor and profiles were measured at an SSD of 100 cm and water phantom depth of 10 cm (Fig. 2). Each detector was positioned at the isocenter and centered on the radiation beam using in-line and cross-line scans to yield the maximum signal intensity. In this work the "daisy-chaining" method 14 was not used.
Doses of 100 monitor units (MU) with 6 MV X-ray beam (WFF) were delivered until three consistent measurements were recorded.
A second set of measurements was completed on a different day and the average "corrected" (using factors from the protocol) and "uncorrected" output factors values were obtained as defined in Eqs.
(1) and (2). While the nominal field sizes are stated in this work the field sizes were measured using in-line and cross-line scans, and used to determine the correction factors to be applied.

Corrected OF ¼
Detector reading; cone or small field Detector reading; reference field Â k TRS À 483 : Table 26 ð Þ   Table 1, and an intercomparison of their measured output factors was completed for the circular fields only.

3.B | Relative standard deviation (RSD)
The RSD for circular and square field output factors (corrected and uncorrected, all detectors) was determined, including the percentage difference with and without correction (Tables 2 and   3).   The corrected output factors for four PTW 60019 microDiamond detectors were compared for the five stereotactic cone fields. Six corrected output measurements (three each from two separate days) for each detector were completed for all cone sizes and the average used ( Fig. 7, Table 4).
3.E | The small field output factor uncertainty budget Sources of uncertainty and their magnitude were identified, and a small field output factor uncertainty budget was prepared showing the combined relative standard uncertainty for circular and square fields for each detector type investigated. The uncertainty budget includes type A and B components, with data from the ARPANSA Australian Clinical Dosimetry Service (ACDS) used to determine some of the type A values. 15 Detectors are divided into four classes as defined in the TRS-483 protocol; microDiamond/unshielded diodes, shielded diodes, micro-ionization chambers (Micro-IC) and mini-ionization chambers (Mini-IC) ( Table 1). The uncertainties in the measurements for the reference fields (cone fields; 3 cm × 3 cm and 6 cm × 6 cm, square fields; 10 cm × 10 cm) and circular and square field measurements are presented and summated in quadrature (Tables 5 and 6), according to the GUM. 16 Explanations for the terms used and how they were determined are presented after the tables.

| 101
The "grey" part of the table is for ionization chambers only, with k T , k P and k H listed as a type B uncertainties. The "blue" section of the table refers to uncertainty measurements related to the reference fields; 3 cm × 3 cm and 6 cm × 6 cm for cones and 10 cm ×  and was found to be 0.01%.
The "yellow" section of the table refers to the uncertainties for the small field measurements. The statistical uncertainty in the charge measurements in the small field (type A) is the maximum relative standard uncertainty for all different field sizes measured.
Whereas, the k small values (a term we derived) are a type B uncertainty, taken directly from the TRS-483 protocol, Table 37 The k small error due to the measurement of the full width half maximum (FWHM), refers to the reproducibility for each square field and cone field size. The error in the field size measurements will contribute to error in the selection of the "k" value from Table 26 of Quadradic summation of Type A and Type B uncertainties was completed for each detector in the "purple" section. Both types of uncertainty were finally combined in quadrature to give the total relative standard uncertainty in the "green" section, and are shown in    Uncorrected output factor (square field) -relative to microD 1  Reasons for this difference with the photon diodes could be attributed to individual detector differences or could be related to the fact that both diodes are shielded, unlike the other diodes investigated in this work and thus have more uncertainty in k s (Table 1).
Shielded diodes are known to overestimate dose relative to water, 17 and exhibit greater perturbations in small field measurements due to the additional metallic layer present around the active volume.
Higher uncertainties in the correction factor are caused by the attenuation of low-energy photons, and simultaneous increase in contributions from electron scatter. 2,[17][18][19] These effects contribute to make larger and more uncertain correction factors.
The uncorrected output factor values measured in this work agree with previous work by Godson 12 who used the IBA EFD, IBA PFD, and PTW 60018 SRS diodes and Pinpoint PTW 31014 ionization chamber. Cone diameters ranging between 10 and 40 mm (in 5 mm increments) and field sizes between 1 cm × 1 cm and 10 cm × 10 cm (in 1 cm × 1 cm increments) were examined, at the same SSD and depth as this investigation. Overall Godson 12 reported reasonable consistency in uncorrected output factors (for all detectors) when using field sizes ≥2 cm × 2 cm. Whilst no correction factors were applied to the results, it was reported for smaller cone and field sizes that the IBA PFD diode over-estimated the output factors, as occurred in this study. These results confirm that larger differences between detectors occur when using smaller field and cone sizes, and that shielded diodes have higher uncertainties due to their construction (namely due to the extra metallic layer).
This work also agrees with the findings by Shukaili, 11 where the TRS-483 protocol correction factors were applied to the IBA-SFD detector used for stereotactic cone measurements (5-40 mm), and compared with EBT3 film and a DUO detector (an in-house design consisting of two silicon diode arrays). Differences in detector and film responses reduced from 5.7% to 2% for the 5 mm cone, with an average agreement of ±0.8% for all 12 cone sizes investigated (after correction). Shukiali, 11 refers to the recent AAPM practice guidelines, which recommends SRS-SBRT annual QA for output factor tolerance is ±2% from baseline for >1.0 cm apertures and ±5% from baseline for ≤1.0 cm apertures. 20 The combined relative standard uncertainty values determined for all detector types in this work (Tables 5 and   6, Fig. 8) are within these limits; ≤1.31% for all cone and square field sizes examined, except for the mini ionization chamber (CC04) measurement, which was; 2.54% (10 mm cone) and 2.53% (1 cm × 1 cm square field) (Fig. 8).
In general, the RSD values for the corrected output factors reduced (for all detectors) (Tables 2 and 3), with the percentage difference between the corrected and uncorrected values decreasing with increasing cone and field size. The largest reduction in RSD was for the 10 mm cone; 1.7% (uncorrected; 2.3%, corrected 0.6%) ( and compared to investigate intra detector variations (Fig. 7, Table 4).
The average of six measurements for each detector showed good

4.C | The small field uncertainty budget
Lastly, the uncertainty budget for the measurement of small field output factors was determined and its components quantified (Tables 5 and 6). The combined relative standard uncertainties are summarized for both circular and square fields (Fig. 8), and the expanded uncertainty (k = 2) applied as error bars to Figs 3(b) and 4(b) and Fig. 9. The largest sources of uncertainty were; k small (which is the uncertainties in the output correction factors stated in the protocol) and ranged between 0.30-3.60% for circular fields (Table 5) and 0.30-2.50% for square fields (Table 6). Tolabin 22 also reported this in their small field uncertainty budget for square fields (0.5 cm × T A B L E 5 The relative standard (RS) uncertainty for all components (A and B) in the measurement of circular fields.    which was determined using the in-line and cross-line profiles for each detector type scanned at each field or cone size. Its magnitude for each detector type ranged between 0.10-0.98% for circular fields (Table 5) and 0.14-0.67% for square fields (Table 6). Interestingly, Tolabin 22 estimated this uncertainty (called µ scan ) as much lower with a range between 0.001 and 0.012% uncertainty for all four detector types investigated. As Tolabin 22 does not state the CAX positioning limit, this difference could be due to applying a smaller positioning error (0.1 mm), which would yield lower uncertainties particularly for steep gradient profiles.
Overall the uncertainties increased as the field or cone size decreased (Fig. 8) as was expected, and in general solid state detectors yield smaller uncertainties compared to the micro and mini-ionization chambers (10-50 mm circular fields and all square field sizes) ( Fig. 8), which agrees with the budget prepared by Tolabin. 22 This is most evident for the 1 cm × 1 cm square fields with the microDiamond/unshielded diodes having a combined relative uncertainty of 0.78%, shielded diodes 0.88%, while the micro and mini-ionization chambers yield 1.31 and 2.53%, respectively.
The consistency between different detectors was assessed by examining all detector output factor measurements at each circular and square field size (Tables 5 and 6, Fig 9) after applying the expanded uncertainty to each result. All circular and square field size output factor measurements showed agreement within uncertainties [Fig 9(a)], except for the 15 mm circular field [Fig 9(

Corrected output factors
(a) Corrected output factors for 7.5 mm circular fieldsuncertainty agreement F I G . 9. Plots of the output factors at the indicated circular field size are shown with horizontal displacement to allow each individual detector to be easily identified. Agreement within uncertainties (a) is shown for the 7.5 mm circular field size by the dashed green line passing through all error bars, and was seen for all detectors and field sizes examined except for the 15 mm circular field size (b), which was the single case of nonagreement. The maximum difference between detectors is shown by the green dashed lines.