3D printed brachytherapy jig for Reference Air Kerma Rate calibration

3D printing in modern radiotherapy allows users the ability to create custom devices which can be a valuable tool for use in brachytherapy source calibration. Radiotherapy centres may verify their brachytherapy source activity with a calibrated Farmer chamber. For this purpose, a jig was designed, 3D printed and commissioned for in-air source strength calibration. Measurements on four afterloaders with varied equipment and environments were completed. A full uncertainty budget was developed and measurements with the in-air jig were consistently within 3% of the certificate source strength, and within the 4.1% combined uncertainty for comparing a well chamber measurement (1.7%) with the in air jig (3.75%). By creating a jig that is able to be customised to multiple catheter sizes and cylindrical chamber designs, centres can be provided with the option of independently checking their source strength with ease and for little cost.


Introduction
Radiotherapy centres that provide brachytherapy treatments should have the ability to independently verify the source strength, frequently specified as the Reference Air Kerma Rate (RAKR) and Apparent Activity, provided by the manufacturer [1]. The International Atomic Energy Agency (IAEA) recommends this verification use RAKR to specify the activity of gamma sources [2]. A number of different detector types are able to undertake this calibration though most often a well chamber is used [3,4]. In many countries, centres are required to ship well chambers overseas for calibration, since not all local standards laboratories maintain a brachytherapy standard or provide a well chamber calibration service [5].
Because the RAKR is directly related to the dose received by a patient it is prudent to have an independent dosimetry system to check against and verify the primary method for calibration. Further to this, having an independent dosimetry system for a brachytherapy source can aid with establishing a mean ratio between the locally measured and vendor specified RAKR which can function as an early indication of problems with the calibration system [6]. Moreover, when sending well chambers overseas for calibration, centres may experience a period of time where they do not have a dosimetry system for calibrating brachytherapy sources. The ability to use a traceable calibrated Farmer chamber provides an easy solution to both challenges; the Farmer chamber can be used both to verify the well chamber measurement and to provide source calibration checks when the well chamber is not available. This method is in accordance with IAEA recommendations for using a cylindrical chamber, such as a Farmer chamber, to calibrate a brachytherapy source [2].
Where primary standards laboratories are able to calibrate cylindrical chambers at energies either side of the Ir-192 mean energy, a correction factor can be produced 1 3 for Ir-192 by interpolation. This approach is recommended by the IAEA [2]. The Australian Radiation Protection and Nuclear Safety Agency (ARPANSA), for example, is able to calibrate cylindrical chambers for reference photon dosimetry in beam qualities 250 kV and 1.25 MeV Co-60 gamma rays. An interpolation between these energies can then be used to calculate an estimate for the N k correction for Ir-192, which decays via gamma decay with an average energy of 397 keV [2].
Using the interpolated N k correction for Ir-192, the IAEA formalism can be followed for calculation of RAKR. This formalism defines RAKR at a distance of 1 m. This 1 m measurement in not always practical due to low signal and possible high leakage currents of ionisation chambers used. According to the IAEA formalism [2], the RAKR can be determined from measurements with a cylindrical chamber at a recommended optimal distance of 16 cm.
Use of the IAEA formalism in conjunction with a calibrated Farmer chamber is subject to increased uncertainties in comparison with well chamber measurements [4,7,8]. When using a cylindrical chamber in-air to calibrate a brachytherapy source, errors can manifest in the way of set up reproducibility, scatter corrections (including lack of air scatter correction [9]), air attenuation factors and source-to-chamber positional accuracy. These errors and uncertainties can be accounted for and minimised with a reproducible and robust set up.
The use of jigs to enable reproducible Farmer chamber measurements has been investigated previously, using both commercially available [10,11] and in-house designed devices [4,7]. However, although the use of 3D printed jigs for non-reference brachytherapy dosimetry has recently been reported in the literature [12], none of these examples have utilised a 3D printed jig for the purpose of absolute dose measurements for a brachytherapy source using the IAEA protocol.
3D printing in radiotherapy is a useful tool for optimising clinical practice and workflow [12][13][14][15]. The speed and accuracy with which jigs can be printed are desirable for radiotherapy departments, particularly those that already have a 3D printing programme set up. This use of 3D printing to address a clinical need provides a quick, cheap and effective solution to alternative jigs available for brachytherapy in-air calibration.
By characterising components of the in-air calibration method to a high level of precision, brachytherapy centres can achieve a reliable measurement of the RAKR of brachytherapy sources without compromising accuracy. The ability to independently verify the strength of a brachytherapy source provides a quality assurance and external audit check which is an important aspect of quality radiation delivery. For this reason, it is necessary for a locally fabricated jig to be tested in various contexts and with changing equipment to ensure reproducible and reliable results.
The objective of this study was to design and fabricate an in-air jig using 3D printing methods, characterise all associated uncertainties and perform repeat measurements for different Ir-192 brachytherapy delivery systems, to evaluate the reliability and robustness of the 3D printed RAKR jig.

Design and fabrication of 3D printed jig
The jig was designed to be customisable for use in different radiotherapy centres, allowing for various brachytherapy afterloaders, catheters, cylindrical chambers and measurement methods. The pieces that held the chamber and catheters were all able to be interchanged with counterparts of various sizes, so that a variety of chambers and catheters could be accommodated with the same base frame. The cavities for holding the catheters and chamber were defined using known dimensions published by vendors with suitable tolerances added. Tolerances were optimised based on a series of test prints, whereby an iterative approach to determine the most reproducible and appropriate dimensions for equipment to fit was completed.
The jig, shown in Fig. 1, was designed in Tinkercad (Autodesk Inc.) and printed with 1.75 mm polylactic acid (PLA) filament on a Raise 3D Pro 2 dual extrusion printer (Raise 3D Technologies, Irvine, USA), using the settings listed in Table 1. To reduce scatter, PLA support structures were only introduced when required. For local testing, the jig was initially created for use with a PTW 30013 Farmer chamber (PTW, Freiburg, Germany) and 2 mm diameter, plastic interstitial needle. The design and fabrication process was then repeated for additional catheter sizes (between 1.2 and 3 mm diameter).
For a combination of Ir-192 sources and Farmer type chambers, the optimal RAKR measurement distance has been shown to be 16 cm, though measurement distances should be selected between 10 and 40 cm [2]. The main jig was designed so that the chamber could sit at three distances from the source; 16, 20 and 24 cm. This allows repeated measurements to determine RAKR from different distances. An attachment for the jig was also created to allow for measurements using a seven-distance scatter estimate. This provided a further four positions for the chamber to sit at 30, 34, 38 and 42 cm from the source.

In-house uncertainty evaluation for 3D printed jig
After completion of 3D printing of the initial version of the jig (for PTW Farmer chamber and 2 mm needle), a visual inspection of the parts was performed and physical measurements of dimensions were made. Testing included assessment of geometric accuracy using calipers, assessment of fit for various needles and the PTW 30013 Farmer chamber, as well as the fit of the support arm and robustness of connections. Gentle manual manipulation was used to ensure the jig did not separate when weight was placed on joints. This was completed to ensure that when the source moves in and out through the catheter, the jig would not deform or separate. Connections that were slightly loose due to printer tolerances could be tightened using adhesive tape and connections that were too tight could be adjusted by filing.
Although the jig was printed with a comparatively low in-fill density (Table 1), the proximity of jig components to both the chamber and the source (see Fig. 1) made it important to establish the potential for scatter from the jig to affect the RAKR measurement. This test was performed by comparing scatter correction factors calculated with and without inclusion of jig scatter effects. A scatter correction without jig effects was calculated using Chang et al's empirical scatter estimate [9,16], which assumes that scatter comes from the surfaces bounding the room in which the measurement is made (walls, ceiling, floor) and therefore relies on the room dimensions to calculate the scatter correction. Scatter corrections that take jig scatter into account (along with wall, ceiling, floor and other sources of scatter in the room) were evaluated using physical measurements at several set distances from the source. Specifically, additional data was measured for seven distances as per IAEA formalism, by using the purpose-designed extension to the jig which allows seven positions for the source to chamber distance. The seven distance measurement data were analysed by developing a python script using SciPy [17] that used an established least squares method [18,19] to derive a constant from the relationship between primary and scattered contributions to the total integrated charge measurement [20]. A two distance estimation of scatter was also performed, per Butler et al. [10], as a secondary verification of the potential magnitude of jig scatter.
As part of the local preliminary testing process, an uncertainty budget for the jig was developed from guidelines in IAEA TECDOC 1585 and uncertainty budgets that have previously been included in brachytherapy literature [21,22]. TECDOC 1585 [23] provides guidance to standards laboratories regarding the assessment and reporting of uncertainty in measurements with reference to the ISO/IEC Guide 98-3:2008, colloquially referred to as the ISO-GUM method [23,24]. The TECDOC 1585 document provides an example of uncertainty analysis for RAKR calibrations which was used as a template to begin the uncertainty analysis used in this study [23]. Sources of uncertainty were initially broken down with reference to the IAEA in-air RAKR formalism described in the next section (see Eq. 1).
Uncertainty in N K was taken from published uncertainties from derivation of N k for Ir-192 [25]. For this uncertainty contribution and for Type B uncertainties presented   [2]. Because the scatter was derived empirically, the published uncertainties were included [9]. The Kondo-Randolph [27] and [28] tables were used to calculate k n which included an anisotropy factor A KR,pn , isotropic factor A � pn(r) and an A w factor correcting for the material of the inner wall of the chamber. The A w factor was taken from the IAEA TECDOC 1274 [2] values for the PTW 30001 chamber. These values were chosen as they had been used previously for the PTW 30010 chamber [10] and the PTW3 0013 farmer chamber has the same build up cap and wall material as its non waterproof counterpart. The individual uncertainty for each of these components contributed to the overall uncertainty for the calculated 1.006 value for k n , at 16 cm.
In order to asses the total uncertainty affecting comparisons between RAKR measurements made with a Farmer chamber in the 3D printed jig and RAKR measurements made using a well chamber, an assessment of the total uncertainty for the well chamber was also required. This assessment also accounted for Type A and B uncertainties, while appreciating that there was no contributing error for air attenuation, significant scatter contributions, extensive position uncertainties and k n chamber corrections. Polarity and recombination were not corrected for the well chamber measurements as the polarity and bias settings quoted on the calibration certificate were used for measurements; however, a conservative estimate was used in the uncertainty budget.

Multi-centre measurements of RAKR with 3D printed jig
To verify the reliability of RAKR measurements made using the 3D printed jig in a small range of clinically-likely conditions, the jig was used to perform in-air measurements of RAKR using four different Ir-192 delivery systems in three different brachytherapy centres, with results compared to reference well chamber measurements and source certificates. Two different GammaMed Plus units (Varian Medical Systems, Palo Alto, USA) and two Flexitron HDR units (Elekta Ltd, Stockholm, Sweden) were used, with various local well chambers and two different types of needle, as listed in Table 2.
For measurements on each afterloader, the maximum response position was used to measure charge and current for dwell times of 50, 30 and 10 s for a 16 cm source-tochamber distance (assuming 16 cm distance perpendicular from center of source is max response). Transit dose was determined by extrapolation from the three dwell times and was subtracted from the measured values when determining RAKR. Measurements for temperature, pressure, recombination and polarity were also taken during the time of measurement. Electrometer readings were repeated for each length of time to ensure a reproducible and stable response.
Having completed the in-house evaluation of jig scatter effects described in the previous section, scatter corrections were calculated for all data sets using Chang et al's empirical scatter estimate [9,16], using dimensions for each treatment room.
Following IAEA guidelines [2], all required correction factors were applied to calculate RAKR ( K R ) from each set of measurements on each afterloader system, as shown in Eq. (1) where N K is the chamber calibration factor, derived from chamber calibration certificates provided by ARPANSA and using the inverse method recommended by Mainegra-Hing and Rogers [29], M u is the mean temperature and pressure corrected integrated charge measurement, N elec is the electrometer calibration factor, M transit is the transit dose correction, k air is the air attenuation factor, k scatt is the empirically derived scatter correction; k n is the nonuniformity (

RAKR measurements with well chambers
To assist in verifying the accuracy of RAKR measurements performed using the 3D printed jig, all measurements were repeated using well chambers. Well chambers used for verification are listed in Table 2. All well chamber measurements were taken within an hour of the jig measurements with the exception of the Flexitron FT00668, which had to be taken in the week preceeding jig measurements due to time constraints. The dwell time used for the well chamber measurements varied depending on local protocols, which included repeated 60 s measurement, and 50 and 10 s measurements (with a subtraction to account for transit dose). The dwell position for these measurements were all taken at the position of maximum response for the well chamber.
In general, RAKR is calculated with the well chamber using Eq. (3), with additional corrections for the Ir-192 source and applicator if applicable.
Here, N RAKR and N elec are the correction factors for the well chamber and electrometer, taken from their respective calibration certificates, k TP is a temperature and pressure correction factor, and M u and M transit are the mean raw integrated charge measurement and the transit dose correction, respectively. (1) These measurements were also compared against the corresponding source calibration certificates, with appropriate decay corrections (see Eq. (2)).

3D printed jig fabrication, in-house testing and uncertainty budget
The jig was printed successfully using the settings listed in Table 1, resulting in sturdy support system for an appropriately positioned source and chamber, with features as illustrated in Fig. 2.
Caliper measurements of all 2 cm pieces of the jig, which are interchangeable for different catheters and chambers, were exactly 2 cm as designed. The maximum deviation in the longer distances in the print (for example, 16 cm source to chamber distance and total length of the jig) was ≤ 2 mm. This deviation is most likely due to the increased warping contribution due to the large dimensions of the print, in comparison to the smaller 2 cm pieces. This deviation was included in the uncertainty budget.
The addition of a 0.5 mm tolerance to the diameter of each of the cavities in the print resulted in a fit that was secure for each object but not so tight that the equipment would be damaged. When the cube pieces that housed the cavity for the catheters to go into were plugged into the base of the jig, they were generally found to be easily interchangeable and reproducible in position. Pushing each catheter to the end of the cavity in the support and then securing it in place with a small rubber stopper ensured that catheter position remained stable and reproducible, so that certainty of consistent source positioning could be assured once the position of maximal response was determined.
As multiple pieces of the jig were fabricated, to allow for use of different chambers and catheters, slight variations in the printed geometry occasionally led to sub-optimal connections between tightly fitting components, printed despite using recommended tolerances from printer commissioning. To reduce waste, these pieces were kept and modified (either by adding adhesive tape or filing surfaces) to achieve best fit for all parts. The jig should also be assessed for long term robustness through visual inspection and SSD checks , to ensure this uncertainty budget is still applicable.
The comparison of values of k scatt with and without the jig scatter component (i.e. in addition to room scatter) allowed the effect of the scatter due to the jig to the RAKR measurement to be evaluated, as part of the initial in-house jig testing process. The value of k scatt value determined using the empirical method, based on room dimensions without contributions from the jig or other objects in the room, was 0.994. The values of k scatt determined using seven distance and two distance measurements, which incorporated contributions from all scatter sources including the jig, were 0.987 and 0.992, respectively. Comparison against the empirical result shows an increase in scatter (decrease in the value of the k scatt correction) of 0.7% and 0.2% when the jig and other scatter sources are included by using the seven distance and two distance methods, respectively. The potential for the jig and other scatter sources to increase the contribution of scatter to each measured RAKR beyond the degree corrected by the empirical k scatt , especially when measuring in external brachytherapy centres, was therefore incorporated into the uncertainty budget for the jig by assuming a k scatt uncertainty of 1.5%. Table 3 shows the full uncertainty budget for the jig for the measurements on the GammaMed plus afterloader. The full uncertainty budget for the use of the 3D printed jig for RAKR measurements came to a total uncertainty of 3.75% k =2. As expected the uncertainty for the well chamber measurements was less than the jig with 1.7% k = 2 uncertainty, shown in Table 4. As four different well chambers were used, components of the uncertainty budget were taken from the literature as a conservatives estimate to apply across all chambers. The uncertainty for N elec was considered in the M u component of each uncertainty budget. Overall, the combined uncertainty affecting comparisons between RAKR measurements made with a Farmer chamber in the 3D printed jig and RAKR measurements made using a well chamber was calculated at 4.1%. This total combined uncertainty is the uncertainty in comparing an in air jig measurement to a well chamber measurement and is the uncertainty for these two methods summed in quadrature.

Assessment of 3D printed jig reliability
Results in Table 5 provide an indication of the reliability of the 3D printed jig as a tool for measuring RAKR with a calibrated Farmer chamber, by comparing results obtained with the jig to results obtained using well chambers, for the four afterloaders at three centres that were used in this multicentre assessment. Comparison of well chamber and Farmer chamber measurement results in Table 5 shows that the differences between each RAKR measured using the jig and the corresponding RAKR measured using the well chamber were 2.7% (for GammaMed Plus HDR), − 2.2% (for Gamma-Med Plus PDR), − 3.6% (for Flexitron S/N FT00594) and − 2.9% (for Flexitron S/N FT00668). These differences are all within the 4.1% (k = 2) combined uncertainty of the well chamber and jig-based measurements.
Data in Table 5 also indicate that all RAKR measurements obtained with the 3D printed jig were within 3% of the corresponding source calibration certificate values and well within the 5% quoted uncertainty on each of the source calibration certificates.

Discussion
The 3D printed jig proved to be reproducible, easy to set up and inexpensive. The jig was successful in providing an independent measurement of the RAKR for multiple sources with different strengths and various catheters. All Farmer chamber measurements of RAKR made using the 3D printed jig agreed with the certificate value within 3% and agreed with the corresponding well chamber measurements of the same sources within the 4.1% combined measurement uncertainty.
Compared to previous studies measuring RAKR with a Farmer chamber and a commercial or alternative jig, the results using this 3D printed jig are generally in agreement. Bondel et al [4] calculated that the mean percentage deviation for in-air measurements with a locally developed jig and using the seven distance scatter method was −0.94 ± 0.42 . Fourie and Crabtree [11] developed a technique for calibrating source in-air that results in general agreement well within 1.5% from the certificate value, using various chambers and a scatter correction previously established by Butler et al [10]. In this study, the absolute mean percentage deviation for the jig measurements Results for all well chamber and farmer chamber measurements followed a consistent trend with the exception of the GammaMed Plus HDR. This may have been due to variation between the true and certificate reported apparent activities, the relative response of the different well chambers used in the study, or a variation in scatter contribution specific to the room and experimental setup. Long term use of the jig requires consideration of potential changes in the shape or properties of the plastic. These changes might be detected by visual and physical inspections before use or constancy check measurements of sources being replaced. Moreover, for maximum traceability at every measurement, the distances should be verified with a calibrated measuring device (such as a caliper). Uncertainty components were compared with previous estimations for in-air measurements [10,11,18,21]. The uncertainty for N K,Ir-192 was 0.4%, consistent with Butler et al and Fourie and Crabtree's previous work. Conversely, Butler et al's k air estimate for the uncertainty component was lower by 0.1% and k n higher by 0.3% than presented here. The type A uncertainties presented in this work are not consistent with van Dijk et al [21]; however, this could be due to the methodology for measuring type A components. Despite this variation, the total uncertainty in van Dijk et al's study is somewhat comparable albeit smaller at 1.0 % (k = 1) compared to jig uncertainty of 3.75 % (k = 2). This total uncertainty of 3.75 % (k = 2) for the in-air jig in this study is slightly larger than the uncertainty calculations by Smith et al of 2.7% (k = 2), which implemented a seven distance method estimation of scatter in the in-air calculation. The total RAKR uncertainty is also larger than Bassi et al's total uncertainty of 1.5% (k = 2). A contributing factor to this may be the larger scatter uncertainty calculated in this study of 1.5% k = 2. The uncertainty for the well chamber was estimated to be 1.7 % which lies between previous well chamber uncertainty budget results of 1.3 % [37] and 3.2 % [38].
Overall, the RAKR measurements with the 3D printed jig consistently provided a secondary check against well chamber measurements for all sources. Locally, the jig provides a second source calibration method independent from the standard well chamber calibration. Not only is the jig user friendly and easy to produce, it provides useful confirmation of the brachytherapy source calibration certificate which is necessary for treatment with brachytherapy sources.
The jig has been made accessible for download through Zenodo [39]. The process of calibrating a brachytherapy source in-air is not expensive or time consuming with access to a 3D printer. The following steps provide guidance for performing an independent check for brachytherapy sources with an in-air method, using the 3D printed jig evaluated in this study.
1. Ensure centre has required equipment including; cylindrical chamber calibrated for energies higher and lower than the mean source energy (e.g. 250 kV and Co-60 beam qualities), interstitial catheter (preferably 2 mm or 6 french) and a low-scatter measurement surface (wooden table, polystyrene foam block, etc). 2. If using a cylindrical chamber other than PTW 30013 or NE2571 edit the model appropriately. 3. Print the jig with settings from Table 1. Commission the jig as per methods shown in this study. 4. Following the method presented in this paper, find the position of maximum response on the catheter and use this determine correction factors for the chamber, a dwell time of 10 to 20 s will suffice. Using this same dwell position, take integrated charge measurements over 50, 30 and 10 s. 5. Take measurement of room dimensions for scatter correction and complete well chamber measurement within 1 hr of jig measurement. 6. Determine RAKR from measurements for comparison against calibration certificate value, with decay corrections.

Conclusions
The presented work shows how 3D printing can be utilised to create a low cost, easily reproducible jig for brachytherapy measurements with a cylindrical Farmer chamber with minimal effort. The jig is designed to be easily customisable depending on chambers available in brachytherapy centres and was able to determine the RAKR for an Ir-192 source from various HDR afterloaders and sources. Moreover, the jig was tested at multiple facilities to ensure robustness under varied environments. A detailed uncertainty budget was devised to provide a description of the accuracy of the measurements taken and was found to be comparable with previous studies. This supports the use of this jig as an independent source check for brachytherapy centres that do not currently have an in-air calibration solution, or those who are starting up a new brachytherapy programme. This study provides the resources and guidance to implement an inair calibration option in a centre, including a design and method for fabricating an in-air jig that is neither time nor resource intensive, to produce reliable RAKR calibration measurements.