Kyoung Won Jang; Heuijin Lim; Manwoo Lee; Jung Ki Kim; Kyo Chul Shin; In-Ho Jung; Sang Koo Lee; Ki-Hwan Kim; Dong Hyeok Jeong

doi:10.14316/pmp.2025.36.4.193

Abstract

Modeling of the radiosurgery system is required to study dosimetry, dose calculation, and radiation shielding for small radiosurgical fields. In this study, a 3 MV linear accelerator head of the Zap-X^® radiosurgery system was modeled using a Monte Carlo code, and the target thickness and photon beam spot size consistent with the measured dose distribution were determined. The mcnpx^TM (Monte Carlo N-particle eXtended v2.4.0) code was used in the geometry modeling and dose calculations in a water phantom. To determine the correct modeling parameters, the photon energy spectrum and depth dose were calculated for various target thicknesses, and the beam profile was calculated for different photon beam spot sizes and compared with the measured values. The components of the Zap-X^® head were modeled, and the target thickness, along with the photon beam spot size, was determined based on measured dose distributions. The calculated percentage depth dose values closely matched the measured values when the target thickness ranged from 1.8 to 2.4 mm. Optimal agreement between calculated and measured beam profiles was observed when the photon beam spot exhibited a full-width at half maximum of 0.8 mm. Modeling parameters for the ZAP-X^® radiosurgery system head were identified that matched well with the measured data. The established model of the Zap-X^® system will be widely used in radiosurgical beam research.

Introduction

The Zap-X^® system (ZAP Surgical Systems, Inc.) is a stereotactic radiotherapy system based on a 3 MeV S-band compact linear accelerator (LINAC) [1 -4]. One of the key features of this system is that it is a self-shielded radiation therapy device designed to minimize external leakage radiation [3,4]. Additionally, its self-shielding design provides high economic benefits because it does not require a high-cost bunker for high-energy X-ray shielding.

The Zap-X^® system uses 3 MV X-rays, which are lower than conventional therapeutic X-ray energies, has a source-to-axis distance of 45 cm, and employs very small irradiation fields less than 2.5 cm in diameter [3]. Due to these non-standard conditions, additional studies may be required to apply reference dosimetry, including determining the photon quality index and correction factors for ionization chambers [5 -7]. To accurately determine these dosimetric variables, physical quantities that depend on photon energy, such as the energy absorption coefficient ratio and stopping power ratio, are fundamentally required [5 -7]. To determine these quantities, the energy spectrum generated by the treatment device is required. The energy spectrum can be used not only for small field dosimetry but also to study dose calculation algorithms for the treatment planning system (TPS) and to design effective shielding for radiation protection. In other words, energy spectrum information can be used to determine quality correction factors in dosimetry, and Monte Carlo methods can be used to verify the dose calculation results of the TPS [5,7]. It can also be used to determine the required shielding thickness in radiation protection research.

In megavoltage X-ray generators, the energy spectrum is typically obtained through Monte Carlo calculations rather than direct measurements. For Monte Carlo calculations, modeling of the accelerator head is required according to the specifications of the Monte Carlo code [8 -10]. Furthermore, accurate modeling of the treatment machine can be used in a variety of future studies, not only for obtaining the energy spectrum but also for research aimed at improving machine performance. However, modeling requires detailed information about the components, such as materials and dimensions, which are not sufficiently known for the Zap-X^® system.

In this study, the LINAC head of the Zap-X^® system was modeled using the mcnpx^TM (Monte Carlo N-particle eXtended v2.4.0, Los Alamos National Laboratory) code [11]. The purpose of this modeling was to determine the target and source parameters, including the shape of the head and collimator, that best match the measured dose distribution in a phantom for use in future research. Since no detailed published data exists on the photon energy spectrum of the Zap-X^® system, our results may be valuable for dosimetry and dose calculation studies, as well as for further research on radiation shielding.

Materials and Methods

1. Modeling of the Zap-X^® head

Data from the Elekom research team indicate that the Zap-X^® system employs a compact, low-energy electron accelerator, with the mean energy of the accelerated electrons being about 3 MeV [1]. The accelerating column was made of oxygen-free high-conductivity copper and had a total length of 35.4 cm [1]. The cavity structure employed an on-axis coupled standing wave design, with a resonance frequency of 2,998 MHz [1]. Additionally, an insulated tungsten target was used for the beam current monitor, and the dose rate at 45 cm from the target was reported to be 1,500 cGy/min [1 -3].

The basic shape of the LINAC head, modeled using the mcnpx^TM code, and the external shape of the actual head are shown in Fig. 1 [3]. In this modeling, the dimensions of the components were approximate values determined from known photographic data of the Zap-X^® [2]. The difference in dimensions between the actual and modeled head shapes was expected to be small. Since the primary purpose of the head is to shield against leakage radiation from the X-ray target, these differences were not anticipated to significantly affect the dose distributions in the phantom.

The head consisted of a primary collimator, monitor chambers, and a secondary collimator, all of which were surrounded by shielding material, as shown in Fig. 1. In this study, the target and secondary collimator were primarily considered as factors affecting the dose distribution in the phantom, while the surrounding shielding area was modeled in an approximately similar form. The shielding around the head was considered important for radiation protection.

The secondary collimator was a thick disk with a diameter of 15 cm and could select eight irradiation fields ranging from 0.4 to 2.5 cm in diameter using an external motor [3]. The secondary collimator was made of tungsten, which was used in this modeling [3]. In this study, the collimated field with a diameter of 2.5 cm at source-to-surface distance of 45 cm was modeled. The X-ray target, made of tungsten, was located at the end of the accelerating column, although its thickness was not known [1]. The water phantom, with a volume of 20×20×25 cm₃ for dose calculation, was positioned 45 cm from the target surface.

In this study, the entire simulation process for calculating the dose distribution from incident electrons was divided into two steps to improve computational efficiency by separating the acquisition of the photon energy spectrum from the calculation of the dose distribution. Therefore, it was necessary to first determine the thickness of the X-ray target in the head. The target thickness affected the photon energy spectrum, which in turn influenced the depth dose curve in the phantom. The second step was to determine the shape of the photon beam spot on the target surface, as the photon beam spot shape influences the resulting beam profile. One of the main objectives of the modeling was to carry out this process. The next subsection describes the process used to determine these parameters.

2. Determination of model parameters

Monte Carlo calculations were performed in two steps. For a given target thickness, the photon energy spectrum directly below the target was first obtained, and then the percentage depth dose (PDD) curve in the phantom was calculated using the energy spectrum and compared with the measured value. For the energy of the electrons incident on the target, the electron energy distributions published by Weidlich et al. [2] were applied. The graph data from Weidlich et al. [2] were manually converted into numerical values, and the results are shown in Fig. 2.

In the electron energy distribution obtained in this way, the most probable energy was between 3.04 and 3.05 MeV, and the mean was estimated to be about 2.93 MeV. These data were applied to the input file of the mcnpx^TM code and used to calculate the photon energy spectrum. In the mcnpx^TM calculations, the F5 tally (point detector tally) was used. The point detector was positioned 2.4 cm from the target surface, corresponding to the entrance of the secondary collimator.

The photon energy spectra obtained using the mcnpx^TM code for various target thicknesses are presented with their average energies in the results section. The energy spectra were directly used as input data for calculating depth dose distributions in the phantom, and the results were compared with the measured data.

After determining the appropriate target thickness that matches the PDD curve, the next step was performed to match the beam profile. To adjust the beam profile in the phantom, the distribution of the photon beam spot at the target location was adjusted. In this study, the photon beam spot was assumed to have a Gaussian shape defined by its full-width at half maximum (FWHM), and the FWHM consistent with the measured beam profile was determined through iterative calculations.

However, it was difficult to match all values of the PDD and beam profile curves simultaneously. Therefore, the target thickness was determined based on matching the PDD values at depths of 5, 10, and 20 cm to the measured PDD, and the FWHM was determined so that the 80% width of the central axis (CAX) dose at 10 cm depth matched the measured beam profile. The measured PDD curve and beam profiles applied for this modeling were obtained from measurements for a 2.5 cm collimator provided by Zap-X^® system users.

3. Monte Carlo calculations

As mentioned earlier, the mcnpx^TM code was used in this Zap-X^® modeling. This code was chosen because it allows easy input of the geometric structure and, with its mesh tally feature, enables convenient output of the dose distribution. In the head modeling, components such as the target, primary collimator, and shielding structures were represented using cylindrical and spherical geometries, while the secondary collimator was modeled using cylindrical and conical geometries.

In the physics card (phys:e, phys:p) settings, the default options, including coherent photon scattering, were used. However, for photon spectrum calculations at each target thickness, the bremsstrahlung control value (BNUM) was set to 10 to enhance bremsstrahlung photon production. In this calculation, 2 million histories were applied, and the statistical uncertainty of the calculation results was less than 0.5% in the region of interest (high-count bins).

In calculating the depth dose and beam profile in the phantom, the output values were obtained using the mesh tally function known as TMESH. The voxel size for the depth dose calculations was set to 0.25×0.25×0.20 cm₃. In the beam profile calculations, the voxel sizes were set to 0.25×0.05×0.20 cm₃ for the steep gradient region and 0.25×0.10×0.20 cm₃ for the uniform region.

The point source geometry was used to determine the direction of the emitted photons in the dose calculations within the phantom. To account for scattering inside the collimator, the field diameter defined at 45 cm from the source was set to 3.5 cm, larger than the collimator field diameter of 2.5 cm. In this calculation, 2×10₉ histories were applied, and the statistical uncertainty of the calculation results was around 0.2%. The cutoff energies for photons and electrons were set at 10 keV (cut:e=0.01 MeV, cut:p=0.01 MeV) in all calculations.

Results

The photon spectrum and calculated mean energy obtained for each tungsten target thickness are shown in Fig. 3.

The mean energy <k> of photons for a given photon energy distribution was calculated by the following equation:

(1)

〈k〉 = \frac{\sum_{i = 1}^{N} k_{i} ϕ_{i}}{\sum_{i = 1}^{N} ϕ_{i}}

where k_i and φ_i are the photon energy and flux of bin i. The mean photon energy in this calculation range is between 0.9 and 1 MeV, as shown in Fig. 3. As the target thickness increases, the proportion of low-energy photons decreases, and the mean energy increases, as shown in Fig. 3. The mean energy increases by approximately 0.02 MeV for every 0.2 mm increase in target thickness.

The PDD curves calculated using the photon spectra are shown in Fig. 4, and the analysis results are presented in Table 1. The maximum dose depth for all calculated PDDs was 0.7 cm, with a difference of 0.06 cm from the measured data, as shown in Table 1. As shown in this table, a target thickness of 2.2 mm matches the measurements well at a depth of 5 cm (−0.46%). However, a target thickness of 2.2 mm provides a better match at a depth of 10 cm (0.25%). Therefore, to compare the overall difference, the root mean square (RMS) difference for the three key depths—5, 10, and 15 cm—was calculated using equation (2).

(2)

RMS difference = \sqrt{\frac{\sum_{j = 1}^{3} {(C P D D_{j} - M P D D_{j})}^{2}}{3}}

In this equation, CPDD_j and MPDD_j represent the calculated and measured values at depth j. When comparing the RMS differences between the calculated and measured PDDs, the smallest error (0.2%) occurs at a target thickness of 2.2 mm, as shown in Table 1.

In modeling, assuming a Gaussian photon distribution for the beam spot, the calculated beam profiles for FWHM values of 0.7, 0.8, and 1.0 mm, along with measured values at a depth of 10 cm, are shown in Fig. 5. As the FWHM increases, the central portion of the profile becomes narrower and the edge slopes become gentler, as shown in Fig. 5. The figure also shows that the best agreement with the measured values occur when FWHM=0.8 mm.

Fig. 6 presents the beam profiles calculated using a photon beam spot size with FWHM=0.8 mm at depths of dmax, 5, 10, and 20 cm in the phantom, alongside the corresponding measured data. The calculated and measured values were in good agreement, as shown in the Fig. 6. Table 2 presents the comparison of the 80% dose width (W80) after normalizing the dose at the CAX to 100% at each depth shown in Fig. 5. In the comparison of calculated and measured beam profiles, the maximum difference was 1.1 mm at dmax, while at other depths it was less than 1 mm, as shown in Table 2.

Meanwhile, a difference exists between the measured and calculated values outside the beam field in the beam profile. Outside the beam field, the calculated values decrease steeply, whereas the measured values decline more gradually. This point warrants further investigation in the future, focusing on the source definition in the calculation model or the detector size in the measurements.

Discussion

In modeling the Zap-X^® system head, the target thickness and photon beam spot were determined to match the depth dose and beam profile for the collimator, which generates the largest field diameter of 2.5 cm. As a result, a target thickness of 2.2 mm and a photon beam spot FWHM of 0.8 mm was determined.

The 80% width of the calculated beam profile was approximately 1 mm smaller. The difference may be attributed to the measurements being performed with a microSilicon diode detector (60023, PTW-Freiburg) having a volume of 0.03 mm³, while the calculations used a voxel volume of 5 mm³. Therefore, using a smaller voxel would likely have yielded better agreement with the measurements. Future research on the Zap-X^® system should extend to secondary collimators of varying sizes.

In this study, the target was assumed to be a single piece of tungsten target, so its shape may differ from the actual one; however, the results remain useful for modeling purposes. In the future, obtaining precise information about the target’s material and thickness could yield better results.

According to Chen et al. [1], the design value of the electron beam spot size for the Zap-X^® system is reported to be 1 mm. This value was not applied in this modeling. Directly calculating the dose in the phantom from the electron beam incident on the target is difficult. Hence, the photon spectrum calculation and phantom dose calculation were performed separately. Consequently, determining the FWHM of the Gaussian-shaped photon beam source was sufficient to calculate the dose distribution in the phantom.

In this study, modeling parameters were obtained for only one collimator size. Therefore, future research is needed to investigate other collimators, which represent a limitation of this study. Modeling the entire range of collimators would require further investigation of the photon beam spot size for each collimator size.

Conclusions

In this study, to model the Zap-X^® LINAC head for future research, the basic shape of the head was modeled using published data, and the unknown values were determined by comparison with measured data. As a result, the target thickness and the FWHM of the photon beam spot on the target surface, which closely matched the measured depth dose and beam profile, were appropriately determined. In this process, the 3 MV energy spectrum of bremsstrahlung photons generated by the Zap-X^® system was obtained. The established Zap-X^® system model can be widely used in research, such as small field dosimetry, radiosurgery dose calculation, and self-shielding analysis.

Notes

Funding

This work was supported by the Dongnam Institute of Radiological and Medical Sciences (DIRAMS) grant funded by the Korea government (MSIT) under grant 50493-2025.

Conflicts of Interest

Ki-Hwan Kim is member of the editorial board of the Progress in Medical Physics, but has no role in the decision to publish this article. The other authors declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Data Availability

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

Author Contributions

Conceptualization: Kyoung Won Jang. Data curation: Kyoung Won Jang. Formal analysis: Ki-Hwan Kim, Jung Ki Kim. Funding acquisition: Manwoo Lee. Investigation: Dong Hyeok Jeong. Methodology: Dong Hyeok Jeong. Project administration: Dong Hyeok Jeong. Resources: Kyo Chul Shin, In-Ho Jung, Sang Koo Lee. Software: Kyoung Won Jang. Supervision: Dong Hyeok Jeong. Validation: Heuijin Lim, Manwoo Lee. Visualization: Kyoung Won Jang. Writing – original draft: Dong Hyeok Jeong. Writing – review & editing: Dong Hyeok Jeong, Kyoung Won Jang.

References

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Fig. 1

Calculation model of the ZAP-X^® LINAC head: (a) model, (b) three-dimensional shape, and (c) actual shape. Reused from the article of Weidlich et al. (Cureus. 2021;13:e13972) [3].LINAC, linear accelerator.

Fig. 2

Electron energy distribution of the electrons incident on the target, as used in this study.

Fig. 3

Photon energy spectrum and mean energy as a function of tungsten target thickness.

Fig. 4

Calculated PDD curves for different target thicknesses and compared with measured data. PDD, percentage depth dose.

Fig. 5

Calculated beam profiles for different FWHM values of the photon beam spot and compared with measured data in water. FWHM, full-width at half maximum.

Fig. 6

Calculated and measured beam profiles at dmax and at depths of 5, 10, and 20 cm in the water phantom.

Table 1

Comparison of calculated and measured PDD values for different target thicknesses

Target thickness (mm)	Calculation (mm)				Measurement (%)

	1.8	2.0	2.2	2.4
D_max depth (cm) [Diff. (cm)]	0.70 (−0.06)	0.70 (−0.06)	0.70 (−0.06)	0.70 (−0.06)	0.76
PDD 5 cm (%) [Diff. (%)]	66.54 (−0.85)	66.63 (−0.72)	66.80 (−0.46)	66.72 (−0.58)	67.11
PDD 10 cm (%) [Diff. (%)]	39.87 (−0.70)	40.11 (−0.10)	40.25 (0.25)	40.35 (0.50)	40.15
PDD 20 cm (%) [Diff. (%)]	15.22 (−1.87)	15.33 (−1.16)	15.48 (−0.19)	15.55 (0.26)	15.51
RMS difference (%)	0.40	0.30	0.20	0.25	-

PDD, percentage depth dose; RMS, root mean square.

Table 2

Analysis of the 80% dose field width at the CAX for each depth in the water phantom

	Scan depth (cm)

	0.7	5.0	10.0	20.0
80% width of CAX dose (cm)
Calculation	2.19	2.40	2.68	3.19
Measurement	2.30	2.50	2.74	3.25
Difference (cm)	−0.11	−0.10	−0.06	−0.06

CAX, central axis.

Approximate Modeling of the Zap-XⓇ Linear Accelerator Head Using mcnpxTM