X-ray radiation device

X-ray radiation devices consist of an X-ray system, a beam-limiting diaphragm, an additional filtration system, guide rails, a positioning system, and a microcurrent measurement system [21]. The X-ray tube model was MG165 equipped with a tungsten target, and the target angle was 20°. Inherent filtration was achieved with the use of beryllium (thickness of 0.8 mm). A high-voltage generator with a tube voltage of 7.5 160 was used. Different reference radiation qualities can be established by adjusting the tube voltage and enhancing filtration by using a filter element with an increased thickness. A beam-limiting diaphragm was used to confine and collimate X-rays. It had an inner diameter of 7 mm, an outer diameter of 6 cm, and a thickness of 4 mm. The material was composed of 93% pure tungsten and 7% pure Ni–Fe. A uniform radiation field was formed at the reference plane to satisfy the measurement and calibration requirements of the air kerma. The principle of the microcurrent measurement system is based on the high-gain negative feedback method; this system consists of an external capacitor, a Keithley electrometer (model 6517), a thermometer, a barometer, and the LabVIEW software program, which is used to achieve automatic control and acquisition functions. The microcurrent measurement system can measure the ionization charge with temperature and pressure corrections in real time.

FAC

The FAC can measure X-rays in the range of 8–100 kV. It serves as the core of the low-energy primary standard of air kerma and can achieve absolute air kerma measurements [22]. The design parameters of the FAC are listed in Table 1. The National Institute of Metrology in China used the FAC in a 2018 international key comparison effort and realized international equivalence [23]. The parallel X-ray beam generated by the X-ray tube enters the FAC through the front diaphragm such that the central axis of the X-ray beam is parallel and equidistant from the upper and lower electrodes. The X-ray beam leaves the FAC through the back hole. The ionization chamber was designed to measure the photon energy in the range of 8–100 keV. The design parameters of FAC are listed in Table 1.

Monte Carlo simulation software

A Monte Carlo simulation software program is typically used to simulate parameters that cannot be obtained directly or are difficult to obtain in the experiment; these parameters are used as a guide and constitute the basis for actual measurements. These include correction factors for electron loss, fluorescence scattering, and diaphragm transmission. In this study, a Monte Carlo simulation was used to obtain the correction factors. The electron gamma shower (EGSnrc) software program, developed by the National Research Council Canada, is typically used for Monte Carlo simulations in radiation dosimetry. Kawrakow [24] quantitatively analyzed the problems associated with EGS4, which made it difficult to simulate accurately the response of the ionization chamber, and proved that EGSnrc addressed these problems and improved the accuracy of the charged particle transport and atomic scattering cross-section. Fu et al. [25] conducted cone-beam computer tomography simulation research based on the EGSnrc software program and verified the accuracy of the developed system. The spectral results obtained using this program showed good consistency with those obtained from the Spektr software program (a computational tool for X-ray spectrum modeling and analysis); the maximum difference was 3.0%, and the mean difference was lower than 2.0%. The DOSXYZnrc program was used to construct the FAC model. Combined with the egs-view visualization program, associated parameters were set, such as the cavity area, exit particle type and angle, medium, and density correction file. The BEAMnrc software program was used to simulate the fluence spectra of X-ray radiation. By selecting the appropriate simulation particle number, density correction file, incident particle source type and energy, cutoff energy of photons and electrons, interaction between particles, and variance reduction technology, a phase space file with the suffix phsp was obtained. The BEAMdp software program was used in combination with the BEAMnrc program, and the generated phase space file was opened in BEAMdp. According to the maximum and minimum energies of the particle source, the corresponding fluence spectral data were generated, including the number of particles and the uncertainty of different energies, and used to realize the calculation and data visualization of the X-ray fluence spectrum. The C++ application egs-fac implemented the transport of the particles in the FAC and calculated the associated correction factors in a self-consistent manner. The correction factors for electron loss, photon scatter, and fluorescence of low-energy and medium-energy free-air chambers were calculated by Burns [26] using the EGSnrc software program. The results were compared with those of the EGS4 software program and the PENELOPE code. Simultaneously, an uncertainty analysis was conducted, providing new values for the correction factors of the Bureau International des Poids et Mesures (BIPM) standards. This software program simulates and calculates the correction factors under the conditions of no vacuum tube, vacuum tube, and air. An FAC ionization chamber was used in this study. Therefore, correction factors without a vacuum tube were selected, namely diaphragm edge penetration, electron loss, scattering, and fluorescence photon correction factors.

Absolute air kerma X-ray measurements

The FAC operates as follows. Continuous X-rays are produced by the X-ray tube after the electron hits the target and enters the FAC through an enhanced filter and a beam-limiting diaphragm. Positive and negative ions are produced by the interaction between the X-rays and air in the cavity; these ions then move to the collecting plate under the effect of the electric field applied between the electrode plates. The resulting ionization current was measured using a microcurrent-measurement system. The air pressure and temperature in the surrounding area must be immediately monitored and corrected for the ionization current measured by the FAC. The air kerma rate was measured using an FAC according to its definition. The modified equation for the air density is given by Equation (1).(1)where ρ₀ is the air density at 273.15 K and 101.325 kPa, and T_a and P_a are the air temperature and pressure during the measurements, respectively.

The air kerma rate was measured by an FAC according to its definition, and the value [27, 28] was calculated using Eq. (2).(2)where V is the effective measurement volume of the FAC, I is the ionization current measured by the chamber, and is the mean energy that produces a pair of positive and negative ions in the air. Moreover, g is the fraction of charged particles lost in the air owing to Bremsstrahlung radiation, and is the product of the correction factors. The physical constants used for the absolute measurement of air kerma rate in the X-rays are listed in Table 2.

Several correction factors affect the design and operation of FAC. These factors were obtained from experimental measurements, Monte Carlo simulations, and recommendations. The correction factors obtained from the experimental measurements are the following: air attenuation correction factor k_a, ion recombination loss correction factor k_s, wall transmission correction factor k_p, polarity correction factor k_pol, and electric field distortion correction factor k_d. Monte Carlo simulations provide correction factors such as the diaphragm transmission correction factor k_dia, the product of the scattering correction factor and fluorescence correction factor , and the electron loss correction factor k_e. Additionally, the product of the initial ion correction factor, the ionization work correction factor , and the humidity correction factor k_h are from the recommendations.

Air attenuation correction factor In the absolute air kerma measurements, the ionization charge was collected in the collection plate of the FAC. The actual measurement position was the geometric center of the front diaphragm hole in the FAC. An air gap exists between the collection plate and the diaphragm of the FAC, where the X-ray energy is attenuated. Several methods are used to obtain the air attenuation correction factor k_a using the vacuum, moving distance, and Monte Carlo methods. In this study, the moving distance method was used to obtain k_a [29]. Equations (3) and (4) were used for calculating k_a.(3)(4)where denotes the mass attenuation coefficient, d is an attenuation length of 10 cm, ρ_20°C is the air density at the temperature 20 ℃, and I₁ and I₂ are the ionization currents measured before and after the attenuation through the air distance, respectively.

Ion recombination loss correction factor To eliminate the inaccuracy of the experimental results caused by ion recombination during the measurement process, which yields a smaller measured ionization current than the true value, an ion recombination loss correction factor k_s is introduced. Ion recombination includes initial and volume recombinations [30]. In this study, the method recommended by BIPM was used to measure k_s [31], implemented by measuring the ionization currents at different tube voltages and currents. Equations (5) and (6) were used for calculations.(5)(6)where k_init is the value of the initial recombination, k_vol is the volume recombination value, and n is the ratio of the polarizing voltage of +1600 V to the tube voltage of the ionization chamber in the area of the plateau with values of 2.5, 3, and 4 for the tube voltages of +640, +533, and +400 V, respectively. Additionally, a₀ is the intercept of the linear fitting equation, and a₁ is the slope of the fitting equation. Thus, k_s can be expressed by Equation (7).(7)where I_v is the ionization current at +1600 V.

Wall-transmission correction factor Some high-energy X-rays enter the ionization chamber from the non-diaphragm hole, resulting in a higher current [32]. To correct the measurements, a wall transmission correction factor k_p must be introduced. The incident diaphragm hole of the FAC was sealed with a lead plug to prevent radiation from entering the incident diaphragm hole. The equation used to measure the is given by Equation (8).(8)where I₁ and I₂ are the ionization currents with and without a lead plug, respectively, and I_leak is the leakage current in the system.

Electric-field distortion correction factor To correct for the electric field distortion, k_d was introduced. Several factors can cause electric-field distortions in the ionization chamber. The collecting plate is not coplanar with the high-voltage plate; scattered photons in the environment enter the ionization chamber through an outer Pb shielding box, and the structure of the voltage divider strips is inconsistent [33]. In the design and processing of the ionization chamber, the maximum possible reduction of the electric field distortion was considered. It is a specific measurement that adds multiple voltage divider strips between the high-voltage plate and the collecting plate so that the electric field of the ionization chamber can be distributed as evenly as possible. When the distance between the collecting plate and the voltage divider strips and that between the voltage divider strips are sufficiently large, the electric field distortion caused by this factor can be ignored [34]. The electric field distortion correction factor k_d was equal to 1.0000.

Initial ion correction factor and ionization work correction factor These two correction factors were introduced for the first time in the ICRU Report 90 [35] as , a value related to the energy of the X-rays. Because increases rapidly at electron energies below 10 keV, FAC requires charged ion balance. Meanwhile, is defined for the incident charged particles released by ionizing radiation and does not include the charges of the initially charged particles. The value of is given in the ICRU Report 90 for monoenergetic photon beams in the energy range of 1–400 keV. For photon energies greater than 300 keV, the product is one. For energies less than 300 keV, the value was calculated using the fluence spectrum. To obtain the value of for the continuous fluence spectrum, the value of for different radiation qualities can be obtained based on simulated fluence spectra.

Polarity correction factor Ideally, the polarity of the bias applied to the ionization chamber should not affect the measurements. To correct for this effect, the measurements with positive and negative polarities were processed using Equation (9), as follows:(9)where I₊ and I_- are ionization currents at the polarizing voltages +1600 V and -1600 V.

Diaphragm transmission correction factor When an X-ray beam passes through a diaphragm, photons that pass through or are scattered by the diaphragm enter the FAC, causing additional effects on the air kerma measurements. This study used a tungsten alloy diaphragm to limit the X-ray beam and reduce the effect of scattering on the measurements. Currently, the correction factor k_dia is typically obtained by using Monte Carlo simulations. In this study, the EGSnrc program was used to simulate k_dia. First, the structural model of the FAC needed to be established; based on the model, E_g denoted the photon energy into the collection area, and E_dia was the deposited energy into the collection area through the hole in the diaphragm. Equation (10) was used to calculate k_dia.(10)Electron loss correction factor If the energy of the incident primary photon is sufficiently high, the charges generated by ionization in the ionization chamber cannot be completely collected, as expected, as a part of them directly hits the upper and lower collection plates. This part of the electron energy includes the electron energy deposited in the plates and the penetrated plates [36]. Equation (11) is used to calculate k_e.(11)where E_e is the deposited energy in the upper and lower collection plates, and E_a is the sum of the deposited energy in the collection volume.

Scattering and fluorescence correction factors Two correction factors are introduced to reduce the influence of additional electrons generated by scattered and fluorescent photons in the ionization chamber on the measurements [37]. Based on equation (12), the product of the scattering and fluorescence correction factors was simulated using the EGSnrc software.(12)where E_sc is the deposited energy of the scattered photons in the collection volume of the ionization chamber, and E_fl is the deposited energy of fluorescent photons in the collection volume.

Humidity correction factor Humidity in the environment changes the ionization current and affects the air kerma. In this study, the humidity correction factor k_h was 0.9980, as recommended by the BIPM [38].

Fluence spectrum simulated by Monte Carlo

Based on the technical parameters of the SRT-100, the tube voltages were set to 50, 70, and 100 kV. The corresponding enhanced filtrations were 0.419, 0.751, and 1.137 mmAl, and the purity was greater than 99.99%. Monoenergetic electrons were selected as incident particles. The cutoff energies of the electron and proton were set at 0.512 and 0.001 MeV, respectively. The ionization chamber was placed 1 m from the focal spot of the X-ray tube, and the number of simulated particles was 10⁸. Three radiation qualities were simulated using the BEAMnrc program, and a model of the X-ray tube and fluence spectra were simulated. The results are presented in Fig. 1; as shown, all the results of every fluence spectrum are normalized according to the maximum fluence data.

Fig. 1Full-screen View

(Color online) (a) Model of the X-ray tube, and (b) simulated fluence spectra of three radiation qualities

Figure 1(a) shows the simulation model of the X-ray machine established using the BEAMnrc program, including the target material, additional filtration, diaphragm, and other parameter settings. Figure 1(b) shows the fluence spectra of three superficial X-ray radiotherapy radiation qualities simulated at 50, 70, and 100 kV. Based on the established X-ray tube model, we selected the density correction database, chose whether to open the relevant particle reactions, and obtained a phase-space file. The phase-space file was opened in the BEAMdp software program and set to generate 200 spectral energy datasets with a minimum particle energy of 0.001 MeV. According to the fluence spectra datasets, the mean energies of the fluence spectra simulated at 50, 70, and 100 kV were 26.2, 34.1, and 44.7 keV, respectively.

HVL Measurements

The half-value layer (HVL) can be used to characterize the X-ray radiation quality, which is divided into the first HVL (1^st HVL) and the second HVL (2^nd HVL) [39]. The 1^st HVL is defined as the thickness of the absorber required when the air kerma rate is reduced to 0.5 times the air kerma rate value in the case in which no absorber is used; the 2^nd HVL is defined as the absorber thickness required when the air kerma rate is reduced to 0.25. The homogeneity coefficient (h) is the ratio of the 1^st and the 2^nd HVLs. A model diagram of the experimental setup for measuring HVL is shown in Fig. 2.

Fig. 2Full-screen View

Model diagram of the experimental device used to measure the half-value layer (HVL) values

According to the measurement method for the HVL in [40], the Farmer chamber PTW30013 was used to measure the ionization current at a distance of 1 m from the focal spot of the X-ray tube, and the absorber was placed at a distance of 0.5 m. Based on the ionization current measured for different absorber thicknesses, the attenuation curve was fitted to estimate the 1^st and 2^nd HVLs. Figure 3 shows the attenuation curves of the three radiation qualities of superficial X-ray radiotherapy in the chamber PTW30013, where the vertical coordinates were normalized according to the maximum ionization current. Table 3 lists the measurements for the 1^st and 2^nd HVLs and h.

Fig. 3Full-screen View

(Color online) Attenuation curves of HVL measurements

Absolute air karma measurements

According to the principle of FAC air kerma measurements, the chamber was fixed at a distance of 1 m from the focal spot of the X-ray tube using a laser and a measuring rod positioning device under established reference radiation quality conditions. The effective measurement center axis of the ionization chamber and the X-ray beam center axis were on the same horizontal line. The FAC was connected to a microcurrent measurement system, and the ionization current was measured using the high-gain negative feedback method. The air kerma rate was measured at a position 1 m from the X-ray focal spot using the FAC by measuring and simulating the relevant correction factors and combining them with the FAC.

The ion recombination loss correction factor k_s was measured at different tube voltages and currents. Five tube currents were set at each tube voltage for each radiation quality, and three tube voltages were simultaneously set at the same time to obtain 15 corresponding ionization currents. The ionization currents for the different tube currents at each tube voltage were processed with an ionization current at a polarizing voltage of +1600 V to obtain the k_s fitting curves. The fitting curves of k_s for three radiation qualities are shown in Fig. 4, and the values of k_init and k_vol are listed in Table 4.

Fig. 4Full-screen View

(Color online) Fitting curves of k_s for three radiation qualities: (a) 50 kV, (b) 70 kV, and (c) 100 kV (curves in blue, red, and black colors in the three subplots denote the variations of k_s as functions of the ionization current at operating voltages of +400 V, +533 V, and +640 V, respectively

Table 4 lists the initial and volume recombination values for the three radiation qualities at different tube voltages. The values were calculated from the ionization current at different tube currents and voltages. The average initial and volume recombination values were calculated. According to Equation 7, the k_s values at 50, 70, and 100 kV were 1.0009, 1.0011, and 1.0007, respectively.

was introduced as a correction factor for air kerma for the first time in the ICRU Report 90. The value of of monoenergetic photons (energy range of 1–400 keV) is recommended, and of the radiation qualities in superficial X-ray radiotherapy cannot be obtained directly. In this study, fluence spectra datasets simulated by the EGSnrc software were used to calculate the products of the radiation qualities. Based on the values of the different monoenergetic photons, the original software program was used to interpolate the products at each energy level in the fluence spectra. Based on the simulated data, the product outcomes kiikw of the fluence spectra were calculated at the three radiation qualities using different interpolation methods, including linear, cubic spline, cubic B-spline, and Akima spline interpolation, as shown in Table 5; the final results were the average results.

The correction factors for the superficial X-ray radiation qualities are summarized in Table 6, and the results for the air kerma rate are summarized in Table 7.

Calibration of transfer ionization chambers

To verify the accuracy of the measured air kerma rate, the transfer chamber was calibrated, and the results were compared with international comparison results. The calibration factor is the ratio between the measured value corrected by the temperature and pressure using the transfer ionization chamber. The standard values were measured using the same reference radiation field. Equation (13), which is used to calculate the calibration factor, is given by(13)where is the standard air kerma rate, and I_tr is the measured ionization current (corrected to 293.15 K and 101.325 kPa) by a transfer ionization chamber.

Considering the fluence of multiple electron scattering and recombination loss, the parallel-plate ionization chamber can reduce the fluence for the measurements of radiation quality at the low-energy X-ray superficial radiotherapy level because of its special structure. Two parallel-plate transfer chambers, namely PTW23342 (0.02 cm³) and PTW23344 (0.2 cm³), were used for the calibration. The effective measurement centers were the geometric centers of the front surfaces of the chambers. During the calibration of the transfer ionization chambers, the ionization current was measured using a connected microcurrent measurement system. It is necessary to focus on the changes in temperature and humidity in the measurement environment. Two transfer ionization chambers were placed in the radiation field, and the reference point of the transfer ionization chambers coincided with the measurement point of the air kerma measured using FAC to implement the subsequent calibration. The effective measurement volumes of the two transfer ionization chambers were low, particularly when the magnitude was approximately 1 pA when PTW23342 was used. When the external environment changes, such as the leakage current, the leakage current changes by 1 fA (ionization current is approximately 1 pA), which leads to an effect of 0.1%. It is necessary to measure the ionization current several times, estimate the average value to reduce uncertainty, and then obtain the calibration factor of the transfer chamber in superficial X-ray radiotherapy radiation qualities. The ionization current was measured under the same conditions as the five CCRI radiation qualities (10–50 kV) using two transfer chambers. In this study, FAC was used to measure the radiation quality of the CCRI air kerma rate (10–50 kV), and the values were considered to obtain the calibration factors. The calibration factors of five CCRI radiation qualities (10–50 kV) and three radiation qualities in superficial X-ray radiotherapy are plotted in Fig. 5.

Fig. 5Full-screen View

(Color line) Calibration results of transfer chambers (a) PTW23342 and (b) PTW23344

The black points in Fig. 5 correspond (from left to right) to 10 kV, 30 kV, 25 kV, 50 kVb, and 50 kVa for the CCRI series, and the red points correspond to 50, 70, and 100 kV for superficial X-ray radiotherapy. According to the measurements, the calibration factors changed for different radiation qualities as a function of X-ray energy. Figure 5 shows the calibration factor curves for the two transfer ionization chambers. There was a significant decrease when the X-ray energy was low, and it changed smoothly at increasing energies. This was consistent with the energy response of the ionization chamber design. Meanwhile, the calibration factors of the two transfer ionization chambers (namely PTW23342 and PTW23344) for the three radiation qualities in superficial X-ray radiotherapy were in good agreement with those of the CCRI radiation qualities. These results are traceable and equivalent to the international results for low-energy X-ray air. The accuracy of the measurement method for the air kerma rate of radiation qualities in superficial X-ray radiotherapy was verified indirectly.

Uncertainty analysis

The FAC measurements and transfer ionization chambers should consider the influence of uncertainty. The measurement uncertainty method was based on the GUM method. This includes uncertainties of Types A and B. The Type A uncertainty was derived from experimental deviations. The Type B uncertainty was evaluated using all the relevant information on the possible variability of the measured quantities [41]. According to the air kerma rate equation, the sources of uncertainty include the volume of the ionization chamber, ionization current, temperature, pressure, ionization current correction factors, and physical constants. For example, the ionization current was measured 10 times repeatedly, and the average value was estimated and used as the final value. The Type A uncertainty of the ionization current originates from the experimental deviation of the 10 measurements. After the analysis, the uncertainties of the associated correction factors measured for FAC are listed in Table 8, and the uncertainties of the air kerma values are listed in Table 9. The calibration factors measured for the transfer chambers are listed in Table 10.

Table 9 shows the results when the FAC was used to measure the air kerma rate; uncertainties were obtained from the correction factors and mean ionization energy . The combined relative uncertainty was 0.47%. Two transfer chambers (PTW23342 and PTW23344) were used for the calibration. Compared with PTW23344, the effective measurement volume of PTW23342 and the measured ionization current were smaller; therefore, the uncertainty of its ionization current was higher. Table 10 shows that the resulting uncertainties in the calibration factors are primarily derived from the air kerma rate and ionization current. The combined relative uncertainties of the calibration factors were 0.50% and 0.48%, respectively. The expanded uncertainties for the calibration factors of the two transfer chambers were 1.00% (k = 2) and 0.96% (k = 2).