Analysis of micro-dose spectrum influencing factors based on tissue equivalent proportional counter

Ionizing radiation dosimetry can predict the intensity of the biological effects of radiation with certain macroscopic physical quantities, such as the absorbed dose. When the object size reaches the cellular level, the discontinuity of the spatial distribution of radiation energy deposition events will be found.¹ Hence, the macroscopic physical quantities based on the statistical average cannot reflect the randomness of this microscopic effect, and the distribution of radiant energy on the micro-scale cannot be obtained. The field of micro-dosimetry was gradually developed to solve this problem since the 1950s.

Micro-dosimetry can accurately describe the microscopic deposition of radiant energy. Its model and micro-dose spectrum are very important. In radiotherapy, through the calculation and measurement of the microscopic energy deposition spectrum, the radiation quality can be obtained. Hence, the appropriate radiation type can be determined, and the in-depth treatment can be carried out. The application of high linear energy transfer (LET) particles in radiotherapy has gradually gained attention, and a lot of studies have been performed, mainly including fast neutron therapy (FNT), boron neutron capture therapy (BNCT), proton therapy, heavy particle therapy, and negative meson therapy.² The experiments carried out by research institutions such as HIMAC and GSI already have made great progress. The Institute of Modern Physics of the Chinese Academy of Sciences (Lanzhou) and the Cancer Hospital of Shanghai Fudan University successively made some studies and experiments on heavy particle therapy.³ 

Waker used the tissue equivalent proportional counter (TEPC) to perform micro-dose spectrum measurements in multiple neutron and photon radiation fields.⁴ Nunomiya et al. performed micro-dose spectrum measurements in a series of single-energy neutron radiation fields.⁵ Zhang et al. used a cylindrical TEPC to perform micro-dose spectrum measurements in the single energy neutron radiation field of the 5SDH-2 accelerator.⁶ 

In recent years, Taylor et al. presented some improvements based on the Geant4 and found that the use of non-default options in conjunction with post-processing allows good matches to be achieved to measured micro-dosimetric spectra.⁷ Werner et al. carried out research on the Monte Carlo method and the method of internal micro-dose spectrum measurement.^8–10 However, their research focused on the measurement model of the micro-dose spectrum and the experimental verification of the model. In their research, the factors that influence the measurement of micro-dose spectrum were only qualitatively described from the aspects of materials and gas composition. In this paper, the simulation method is used in the TEPC design, and the important influence factors are compared and analyzed. Therefore, The TEPC’s structural model and the built-in electric field model are established in this paper based on the GEANT4-MC software, the QT visualization software, and the ROOT data processing software. This paper also analyzes the effects of wall material, the composition of tissue equivalent gas, and the electrode on the micro-dose spectrum. The results can provide a technical basis for the structural design and the processing of TEPC. It can also provide theoretical support for accurate radiation dose measurement and the assessment of human health and safety.

The lineal energy y represents the ratio of the energy that is deposited when one charged particle passes through a specified volume to the average chord length of the specified volume.¹¹ It can be calculated by

In specific volume, there is a distribution of lineal energy y. Formula (2) shows the distribution of lineal energy y, which is represented by F(y) where $y̲$ is the random variable,

The frequency probability density function is the derivative of F(y) to y. Formula (3) shows the function expressed by

where f(y) is the probability of the appearance of the lineal energy within the unit line energy interval near y, and F(y) and f(y) satisfy the normalization condition as shown in the following equation:

The expected value of lineal energy y can be expressed by

The ratio of the absorbed dose is expressed as $ydy$ by the lineal energy between y and $dy$ to the total absorbed dose where $dy$ is the dose probability density of the lineal energy and it is proportional to the product of y and f(y), and the scale factor meets the normalization condition. Formulas (6) and (7) can be expressed as

and

The expected value of $dy$ can be expressed as

The micro-dose spectrum can intuitively express the contribution of various particles to the spectrum, which is convenient for studying the ingredient of the radiation dose.

TEPC can be used as a linear energy transfer (LET) spectrometer because the size of the cells simulated by TEPC is smaller than the range of the ionizing radiation particles. TEPC can distinguish particles with different LET in a mixed radiation field, which is significant for the monitoring and protecting of mixed neutron photon radiation fields. According to the change of the tissue equivalent gas pressure, TEPC can simulate the energy deposition of the radiation in cells of different sizes. Based on the above, the micro-dose spectrum of ionizing radiation can be measured by TEPC.

The neutron source and proportional counter are the main components in the simulation model. The TEPC wall is set to 2.54 mm thick with A-150 plastic with a density of 1.28 g/cm³. The inside diameter of the proportional counter is set to 12.7 mm, and the chamber is filled with methane-based tissue equivalent gas (CH₄ 64.4%, CO₂ 32.4%, and N₂ 3.2%) of 3.86 kPa. The chamber filled with methane-based tissue equivalent gas is defined as sensitive volume, and the voltage of the electric field is 800 V. The shape of the neutron source is set as a circular surface, and its diameter is the same as that of the maximum cross section of the TEPC. The minimum distance from the center of the circular surface to the wall is 15 mm, and the neutron source energy is set to 2 MeV. The number of neutrons is set to 4 × 10⁷ to get a good statistical result. The QGSP-BIC_HP physical list is selected due to the high precision for the neutrons with energy lower than 20 MeV. In the simulation process, objects with small volume and small influence on the radiation field such as anode wire are ignored. Figure 1 shows the simulation model established by Geant4. Figure 1(a) is the TEPC model where the purple part represents the TEPC wall and the yellow part represents the TEPC chamber, and (b) is the particle track model.

The event generator of Geant4 generates 2 MeV neutrons, and they enter the chamber from the outside of the wall, and various kinds of energy deposition events will take place in it. The calculation of energy deposition in the chamber is to accumulate the energy deposition of each step of each source particle in the chamber. The basic elements of TEPC are C, H, O, and N. According to the physical mechanism, the physical process in the simulation mainly focuses on the hadron elastic physical process, hadron capture physical process, and neutron inelastic physical process. Figure 2 shows the block diagram of Geant4.¹² 

In order to test the reliability of this model, three sets of simulations are performed with neutron energies of 2 MeV, 6 MeV, and 10 MeV. The deviation between the calculation result and the literature data is less than 2%, as shown in Fig. 3.¹³ It can be concluded that the theoretical calculation model established by Geant4 is reliable for the micro-dose simulation of TEPC.

A-150 and polyethylene are selected as the wall material, respectively. The simulation is performed under the condition that the gas composition (methane-based tissue equivalent gas) in the chamber is unchanged. Figures 4 and 5 show the micro-dose spectra for different wall materials.

Table I shows that the value of $y¯F$ (average frequency of lineal energy) and $y¯D$ (dose average lineal energy) of A-150 wall material is closer to that of human tissue. The elastic collision between neutron and H is the main interaction, and the proportion of C, H, O, and N will directly affect $y¯D$⁠. The proportion of H, N and the total weight of O, C in A-150 wall material are similar in human tissue. At the 2 MeV energy point, the neutron elastic scattering cross sections of O and C are 3.50 × 10⁻²⁴ cm⁻² and 4.73 × 10⁻²⁴ cm⁻², respectively. The discrepancy between the two elastic scattering cross sections is very small. In the polyethylene wall material, the proportion of H is less than that in human tissue, and the proportion of C is higher. Therefore, the energy deposition is lower in the low-energy region, and it is higher in the high-energy region. The lineal energy average is higher than that in human tissue, and the equivalence of polyethylene to human tissue is poor.

In the simulation of the 1 µm human tissue, the wall materials are set to tissue components, and the equivalent gases are set to propane-based equivalent gas and methane-based equivalent gas, respectively. Figure 6 shows the micro-dose spectrum of different compositions of the equivalent gas. Through the calculation, the deviations of $y¯D$ of methane-based gas and propane-based gas are 4.5% and 5.3%, respectively. The results show that the difference between methane-based equivalent gas and propane-based equivalent gas is small.

The gas multiplication is the main consideration for the design of the electrode structure. Gas multiplication is calculated for the two different equivalent gas with formula (9).¹⁴ Figure 7 shows that the gas multiplication of the propane-based equivalent gas is greater than that of the methane-based equivalent gas in the same gas pressure and voltage condition, and the propane-based equivalent gas can get a wider range of multiplication, which is about three times that of the methane-based equivalent gas. Considering the energy range width of the micro-dose spectrum, the propane-based equivalent gas is more suitable for the measurement of the micro-dose spectrum,

where A = 0.075 cm⁻¹ Pa⁻¹, B = 1.68 V cm⁻¹ Pa⁻¹, G denotes gas multiplication, a denotes the anode radius, b denotes the cathode radius, V denotes the voltage applied, and B denotes the barometric pressure.

The electrode size has an effect on gas multiplication, and the propane-based equivalent gas can exhibit greater gas multiplication. Figure 8 shows that the gas multiplication increases with the size of the electrode when the chamber is filled with propane-based equivalent gas. The multiplication should not exceed 1 × 10⁴. Among the three electrode sizes as shown in Fig. 8, the operating voltage multiplications of the 0.006 35 cm electrode in 240 V and 600 V are 17.2 and 2000, respectively. The micro-dose spectrum from 0.1 µm/K eV to 1000 µm/K eV can be obtained through the cooperation of the 0.006 35 cm electrode and the main amplifier (1–100).

There are many factors that can cause distortion of the micro-dose spectrum. The TEPC simulation model is established and several elements affecting TEPC are analyzed through GEANT4, QT, and ROOT software. The reliability of the model and method is confirmed by multiple sets of verification simulations. Compared to polyethylene, A-150 is more suitable to be set as the wall material for TEPC. Propane-based equivalent gas is more suitable as the tissue equivalent gas of TEPC through comprehensive analysis. In the case that the ideal wall material and equivalent gas have been selected, three electrode sizes are analyzed, of which 0.006 35 cm is suitable as the electrode size of TEPC.

The authors declare that they have no known competing financial interest or personal relationships that could have appeared to influence the work reported in this paper.

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