The linear accelerators, Synergy^® (Elekta AB, Stockholm, Sweden) and Versa HD^TM (Elekta AB), were installed in the two independent institutes, Seoul National University Veterinary Medical Teaching Hospital (VMTH) and Chung-ang University Gwang Myeong Hospital (CAUGH), respectively. Both machines were equipped with the same multi-leaf collimator (MLC) Agility^TM. Despite inevitable uncertainties through the installations, the beam characteristics were expected to be the same in principle because both machines utilized the same type of MLC [1,2]. Moreover, two institutes used the same treatment planning system (TPS), Monaco^® (Elekta AB).

Monaco^® TPS (Elekta AB) can calculate dose distributions based on the Monte Carlo (MC) algorithm [3]. MC algorithm takes advantage of providing a more realistic dose distribution by exploiting particle responses to materials than the model based analytic algorithm [4]. However, the data fidelity depends on the number of particles (history), which is proportional to the time consumption. Nowadays, cutting-edge technologies significantly reduce the required time taken for the MC calculation, but one still needs to optimize the quality of MC simulation data versus the required time [5].

A qualified medical physicist is in charge of the entire beam commissioning stage, including the selection of the measurement system, beam data measurement, and thorough validation. As we exchanged ideas in learning the characteristics of the Elekta linear accelerator and measuring the beam data for commissioning [6], we were curious to see how the calculated beam data reproduces the measured dose distribution. Another interesting point was that independent tools between the institutes measured the beam data. For example, CAUGH mainly measured profiles and percent depth dose (PDD) by using a CC13 ion chamber (IBA Dosimetry GmbH, Schwarzenbruck, Germany) in horizontal setup, while VMTH used Semiflex 31021 (PTW Freiburg GmbH, Freiburg, Germany) in vertical configuration [7]. Moreover, different tools, from the ion chambers to water phantoms, including analyzing software were chosen. Therefore, this study aimed to verify how the other measurement devices affect the agreement between calculation and measurement. Moreover, we also demonstrated how calculated dose distributions matched across two institutes.

1. Beam data measurements

Versa HD^TM in CAUGH was installed accompanying photon beams of 6 MV with flattening (FF) and flattening filter free (FFF), 10 MV with FF, 10 MV FFF, and electron beams of 4, 6, 8, 10, 12, and 15 MeV. Meanwhile, Synergy^® in VMTH was equipped with 4, 6 MV FF photon beams and 6, 8, 10, 12, and 15 MeV electron beams. Among the available beams of the common energies between the two institutes, 6 MV photon beams and 6 MeV electron beams were selected to compare the measurement and calculate based on the MC algorithm.

Beam data commissioning is the process that matches the beam model in TPS to actual beam properties. Monaco^® TPS requires total dose, scatter factors, wedge factors, PDD, and off-axis profiles, in which we compared the PDD and off-axis profiles.

The 6 MV photon beams in field sizes of 2×2, 5×5, 10×10, 15×15, and 20×20 cm² were examined by their PDD and off-axis profiles at a depth of maximum dose (D_max) and 10 cm, where the D_max is a depth of maximum dose along the central axis (CAX). For the 6 MeV electron beams, the PDD, inplane, and crossplan profiles below 1 cm of the water surface were compared with applicators of field sizes: 6×6, 10×10, 14×14, 20×20, and 25×25 cm².

2. Beam data measurement using orthogonal chambers

VMTH used BEAMSCAN^® water phantom (PTW Freiburg GmbH), whose scanning dimension is 500×500×415 mm³, along with WaterTankScans (ver. 4.5; PTW Freiburg GmbH) analysis software. GAUGH used Blue Phantom 2 water phantom (IBA Dosimetry GmbH), whose scanning dimension is 480×480×410 mm³, along with MyQA Accept (ver. 9.0.17.0; IBA Dosimetry GmbH) analysis software. Each institute selects different ion chambers according to the scanning field size (Table 1).

Table 1 . Ion chambers used for the beam data measurement in relative dose distributions from VMTH and CAUGH.

Chamber specifications	Scan field size
	≥5×5 cm2			≤5×5 cm2
	Field chamber	Reference chamber		Field chamber	Reference chamber
VMTH
Chamber (manufacturer)	Semiflex 31021 (PTW)			Pinpoint3D 31022 (PTW)	T-REF 34091 (PTW)
Sensitive volume (cm3)	0.07			0.016	10.5
Chamber radius, length (mm)	2.4 , 4.8			1.45, 2.9	40.8, 2 (depth)
Chamber voltage (recommended) (V)	±100–400 (400)			±100–400 (300)	±300–400 (400)
Nominal response (nC/Gy)	2			0.4	325
CAUGH
Chamber (manufacturer)	CC13 (IBA)			Razor chamber (IBA)	CC13 (IBA)
Sensitive volume (cm3)	0.13			0.01	0.13
Chamber radius, length (mm)	3.0, 5.8			1.0, 3.6	3.0, 5.8
Chamber voltage (recommended) (V)	±100–500 (300)			±100–500 (300)	±100–500 (300)
Nominal response	3.6			0.3	3.6

The most significant difference in the measurement procedure was that VMTH set up the PTW Semiflex 31021 chamber vertically for the scan. In contrast, the PTW Pinpoint3D chamber and IBA chambers were placed horizontally. An effective point of measurement (EPOM) was considered independently for the IBA chambers in CAUGH [8]. However, it was challenging to put the right measurement spot of the ion chamber vertically to the water surface as in the horizontal setup. Thereby the vertical setup was done by the PTW holder relying on the PTW TRUFIX^® detector positioning system (Fig. 1).

Figure 1. Horizontal (left) and vertical (right) positioning of the ion chamber (PTW TRUFIX^® Detector Positioning System).

Measured beam data was post-processed to obtain the correct D_max called EPOM correction and corrected symmetry before the comparison (CAX correction). The electron percent depth-ionization was also converted to PDD following the task group (TG)-51 protocol of the American Association of Physicists in Medicine (AAPM) in both institutes. CAUGH used MyQA Accept for the beam scanning and the post-processing, and the EPOM was corrected in the analysis software. In VMTH, WaterTankScans was operated with automatic beam center and EPOM correction by TRUFIX^® without further specific post-processing.

Absolute output was measured by the same farmer chamber, PTW 30013. During the commissioning, Monaco^® required the total dose output at a source-to-surface distance (SSD) of 90 cm. As both institutes defined 1 cGy/MU (monitor unit) at D_max under SSD of 100 cm following AAPM TG-51 protocol [9], the requested absolute dose at SSD of 90 cm was estimated by applying inverse square law.

3. Comparison with the MC simulation data with Monaco^®

Both institutes were equipped with the Monaco^® (v5.51.10) TPS. After the installation of the beam modeling set by the Elekta modeling team, the simulated beam data became available. The photon beam data was simulated in a virtual water phantom of 50×50×50 cm³ by the MC algorithm with a minimum grid resolution of 0.1 cm and statistical uncertainty of 0.5% per control point. For the electron beam, MC simulation data with a grid resolution of 0.1 cm and a history of 1 million was generated, assuming the same water phantom was used.

Measured beam data were compared with the calculated data, and their similarity was quantitatively evaluated by the gamma analysis. The evaluation was done for each institute. The equation used for the gamma index calculation is written in Eq. (1) [10],

where the squared difference between the measured dose (D_meas) and the calculated dose by MC simulation data (D_MC) is divided by its criterion (σD) and the squared difference between the measurement location (rmeas) and the calculation point (rMC) is divided by its limit (σr). The gamma index combined dose and distance difference in 5–250 mm (5–80 mm) depth for the photon (electron) PDD distribution and within 80% of the field size for the off-axis beam profiles. Here we used a 2% (σD)/2 mm (σr) threshold for the PDD distribution and a 3% (σD)/3 mm (σr) threshold for the inplane and crossplane profiles, respectively, following the criteria used by Elekta beam modeling evaluation report. When the gamma index is ≤1, it is counted as passing the criteria.

The gamma passing rates of the photon beam off-axis profiles were 100% for all the beam data comparisons obtained at CAUGH and 100% for the data except for the inplane profile at 10 cm depth, which was 99.2%, from VMTH.

The PDD distributions of the measured beam data and the calculated MC simulation data at a field size of 10×10 cm² from both CAUGH and VMTH are shown in Fig. 2a and 2b. Inplane and crossplane profiles at the same field size and depths of D_max and 10 cm are shown in Fig. 2c–2j. Calculated gamma indices are shown in the same plots. We additionally performed the gamma analysis between the measured beam data from two institutes, which showed gamma rate of 100%.

Figure 2. Photon beams (6 MV) with field size of 10×10 cm². Measured distributions (green) were compared with the MC simulated distributions (blue) for each institute (CAUGH and VMTH) and the gamma index per point (red) was overlaid. From the top left, PDD of (a) CAUGH and (b) VMTH, inplane and crossplane profiles at a depth of D_max of (c, e) CAUGH and (d, f) VMTH beam data, and those at 10 cm depth of (g, i) CAUGH and (h, j) VMTH beam data. CAUGH, Chung-Ang University Gwang Myeong Hospital; MC, Monte Carlo; PDD, percent depth dose; VMTH, Seoul National University Veterinary Medical Teaching Hospital.

The gamma passing rate for the electron beam comparison of off-axis profiles at CAUGH and VMTH are listed in Table 2 and 3. Unlike the photon beam, off-axis profiles, the electron MC simulation data showed worse fluctuations, and their agreement with the measured beam data is a bit worse even with the 3%/3 mm limits. The calculated electron PDD distributions, however, showed a 100% gamma passing rate compared to the measured PDD distributions in all concerned field sizes between 5–80 mm depth range below the water surface with a 3%/3 mm gamma criterion. Fig. 3 shows the PDD and off-axis profiles from each institute.

Table 2 . Gamma passing rate for electron (6 MeV) beam off-axis profile comparison between measured and calculated data at Chung-Ang University Gwang Myeong Hospital (CAUGH).

Scan type	Applicator size (cm×cm)
	6×6	10×10	14×14	20×20	25×25
Measurement depth (cm)	1	1	1	1	1
Inplane (%)	100	91.4	100	97.5	92.0
Crossplane (%)	100	97.5	99.1	98.8	95.5

Table 3 . Gamma passing rate for electron beam (6 MeV) off-axis profile comparison between measured and calculated data at Seoul National University Veterinary Medical Teaching Hospital (VMTH).

Scan type	Applicator size (cm×cm)
	6×6	10×10	14×14	20×20	25×25
Measurement depth (cm)	1	1	1	1	1
Inplane (%)	95.9	93.8	91.2	100	100
Crossplane (%)	100	100	97.3	100	99.5

Figure 3. Electron beams (6 MeV) with a 10×10 cm² applicator. Measured distributions (green) were compared with the MC simulated distributions (blue) for each institute (CAUGH and VMTH) and the gamma index per point (red) was overlaid. From the top left, PDD of (a) CAUGH and (b) VMTH, inplane and crossplane profiles at a depth of 1 cm of (c, e) CAUGH and (d, f) VMTH, respectively. CAUGH, Chung-Ang University Gwang Myeong Hospital; MC, Monte Carlo; VMTH, Seoul National University Veterinary Medical Teaching Hospital.

Although the beam data measurement procedure was determined, there were a few differences depending on the physicist’s choice in this study. While the VMTH used a pinpoint 3D chamber for field sizes 2×2, 3×3, and 4×4 cm² only, CAUGH used the results obtained by a small chamber ion chamber, IBA razor, for field sizes up to 5×5 cm². Moreover, VMTH used same D_max, which was taken from a field size of 10×10 cm² of PDD measurement for profiles in both small and large field sizes. CAUGH, however, used the D_max taken from the field size of 2×2 cm² for profiles in field sizes ≤5×5 cm² and then used D_max at field size of 10×10 cm² for profiles in a larger field. Comparing the result, this difference was insignificant in the characteristics of the measured beam data.

Despite several differences during the measurement, measured beam data between the two institutes showed a good agreement. In other words, whichever tools with subtle differences were used, the beam characteristics were proven to agree. The comparisons between the measured data and the MC simulation data after installing beam modeling were also in good agreement. Although the electron MC simulation data showed slightly worse agreement than the photon beam, they were still under the tolerance limits of the Monaco^® commissioning [11].

Comparing the electron beams, one curious observation was that agreement between the measured beam data from both institutes was better than the agreement between the measured and simulated beam data for each institute (Fig. 3). Although the PDD distributions from both institutes look very similar, the calculated PDD distal fall-off went more rapidly for VMTH and more slowly for CAUGH. Despite the differences, the gamma passing rate of PDD distribution from both institutes was still 100% in the 3%/3 mm gamma criterion.

We observed that the electron MC simulation showed more fluctuations than the photon MC data. This is an intrinsic issue in simulating particles with the MC. As it simulates particles one by one, the distribution quality is proportional to the number of particles used in the simulation, which is set by the number of histories in Monaco. One has to compromise the time and resources consumed for the large number of particles to be simulated versus the quality of the dataset.

While two independent institutes were equipped with totally different measurement systems in the beam commissioning stage, they exhibited good performances with gamma passing rates of more than 91% in calculation and measurement. Despite the different measurement systems, no significant dosimetric differences were found.

This work was supported by a grant from the National Research Foundation of Korea (NRF) funded by the National Research Foundation of Korea (NRF) and Korean Association for Radiation Application as a part of the Radiation Technology Commercialization Project of the Korean Ministry of Science and ICT (NRF-2019M2D3A2060217, Technology Transfer and Commercialization in the Radiation fields).

The authors have nothing to disclose.

The data that support the findings of this study are available on request from the corresponding author.

Conceptualization: Chang Heon Choi and Jung-in Kim. Data curation: Chang Heon Choi, Lee Yoo, Hwajung Lee, and Minsoo Chun. Formal analysis: Geum Bong Yu and Minsoo Chun. Funding acquisition: Chang Heon Choi and Jung-in Kim. Investigation: Geum Bong Yu and Minsoo Chun. Methodology: Minsoo Chun. Project administration: Minsoo Chun. Resources: Jihye Choi, Soyeon Kim, Yongsik Kim, Do Hoon Oh, Hwajung Lee, Lee Yoo, Minsoo Chun, Geum Bong Yu, Jin Dong Cho, Euntaek Yoon, Hyung Jin Choun, and Chang Heon Choi. Software: Geum Bong Yu, Lee Yoo, and Minsoo Chun. Supervision: Minsoo Chun. Validation: Geum Bong Yu and Minsoo Chun. Visualization: Geum Bong Yu. Writing – original draft: Geum Bong Yu. Writing – review & editing: Minsoo Chun.