Investigation of combined degrader for proton facility based on BDSIM/FLUKA Monte Carlo methods

Man-Fen Han· Jin-Xing Zheng · Xian-Hu Zeng· Jun-Song Shen

Abstract The significant advantage of proton therapy over other particle-based techniques is in the unique physical characteristics of the Bragg peak. It can achieve a highly conformal dose distribution and maximize the probability of tumor control by varying the irradiation energy. Most proton facilities use cyclotrons for fixed energy beam extraction and are equipped with degrader and collimator systems for energy modulation and emittance suppression.However, interactions between charged particles and degrader materials inevitably cause beam loss and divergence and deteriorate beam performance, which present great challenges for downstream transport and clinical treatment. In this work,we investigate a method of energy reduction by combining boron carbide and graphite in a degrader to obtain greater beam transmission at lower energy. The results demonstrate that the beam size and emittance at the exit of the combined degrader diverge less than those of multi-wedge one in the energy range of 70 - 160 MeV. Correspondingly, the transmission efficiency after the first dipole also shows improvements of 36.26% at 70 MeV and 70.55% at 110 MeV. As a component with a high activity level, the degrader causes additional ambient radiation during operation. Residual induced radiation even remains several hours after system shutdown. Analysis of material activation and induced radiation based on 1 h irradiation with a 400 nA beam current shows that the combined degrader has a definite advantage in shielding despite producing more secondary particles. Both radioactivity and average ambient dose equivalent are reduced by 50% compared with the multiwedge degrader at the important cooling time of 1 h.After 12 h and 24 h of cooling, the radiation levels of degraders decrease slightly due to the presence of long half-life residual nuclides. The average dose generated from the multi-wedge degrader is still 1.25 times higher than that of the combined one.

Keywords Proton therapy · Degrader · Boron carbide ·Transmission efficiency · Radionuclide · Ambient dose equivalent

1 Introduction

As part of a cooperative construction project, JINR(Russia) and ASIPP (China) built a proton therapy facility in Hefei,China,in 2016.It contains advanced pencil beam scanning technology and aims to meet the demand for clinical proton therapy [1]. The SC200 proton therapy facility is equipped with a compact isochronous superconducting cyclotron that will produce a defined energy beam of 200 MeV and consists of two beamlines that guide the beam to a gantry treatment room and fixed treatment room. To ensure highly conformal irradiation in the direction of tumor depth, an energy selection system is performed in beam trajectory to modulate the fixed energy extracted from the cyclotron to therapeutic requirement regions 70 - 200 MeV (Projected Range 4.075 - 25.93 g/cm2for water) [2]. In the terms of superficial tumors, additional range shifters are inserted between the nozzle and patient to achieve clinical energy levels of ＜70 MeV. The principle of energy modulation depends on the interactions between charged particles with materials. Inelastic collisions, such as ionization and excitation, are dominant factors in energy loss. Multiple Coulomb scattering and nuclear fragment reactions result in further reductions in primary proton flux and the generation of secondary particles, consequently inducing inherent emittance growth and momentum spread [3, 4].Therefore, a set of collimators and momentum slits are used after the degrader to constrain the beam parameters within acceptable specifications for the downstream transport line. Limited acceptance implies that there is significant intensity loss during beam collimation, especially at low energies where the combination of treatment time and beam intensity is very important,which may cause material activation and radiation damage to surrounding equipment.Typically, degrader system requires high transmission efficiency to maintain an acceptably high dose rate during treatment.In particular,the concept of FLASH therapy has been proposed [5, 6].

There is no doubt that materials with low atomic numbers are suitable for use in degraders because of their great radiation length, indicating less beam divergence and emittance growth, predicting higher transmission efficiency. Most proton therapy facilities use multi-wedge degraders composed of high-density graphite. As an alternative, some institutes employ beryllium to minimize emittance growth. Nevertheless, high neutron yields and chemical toxicity are not negligible hindrances in beryllium applications [7, 8].

In recent years, boron carbide (B4C), depending on its unique properties, has shown tremendous potential as a degradation material. Experimental results from the Paul Scherrer Institute show a 37% improvement in transmission efficiency when using a B4C block (ρ = 2.51 g/cm3)to reduce 250 MeV proton energy to 84 MeV in comparison with a graphite degrader set to that energy [9].Actually, the issue with B4C wedge-shaped degraders is their high Mohs hardness (9.3), which restricts their processing. To eliminate this limitation, HUST-PTF studied the effect of using a B4C/graphite composite (BGC)material. The efficiency increased by 15.9% at a 70 MeV degrader setting with a 40% boron in BGC [10].

Considering the higher transmission efficiency and engineering feasibility comprehensively during energy modulation,this paper presents a novel combined degrader structure in the form of a double graphite wedge and two B4C blocks. The analysis not only includes comparison of the influence of multi-wedge graphite degrader and combined one on the downstream beamline performances, but also investigates the radioactive contamination resulting from nuclear fragment reactions between protons and materials under the maximum energy degradation. Accurate particle-matter interaction models of the degraders are developed in BDSIM and FLUKA Monte Carlo methods for specific evaluation. The work provides theoretical guidance for the optimization and maintenance of SC200 degrader.

2 Experimental section

2.1 Beamline layout and degrader properties

The proton beam extracted from the cyclotron is focused on the entrance of the degrader by four quadrupoles (Q1-Q4).In a high-density graphite degrader with a total length of 137.5 mm,the energy varies continuously depending on the thickness of the inserted graphite. Due to the multiple scattering of protons in the material, the beam divergence and emittance increase at the exit of the degrader.A set of collimators are subsequently required to suppress the beam size and divergence angle.Figure 1 illustrates the layout of the SC200 facility in detail[11].A copper collimator Col2,placed 2 mm behind the degrader,is matched with Col4 to limit the maximum beam emittance to within 16 πmm·mrad. Quadrupoles (QE1, QE2) act as the beginning of the achromatic section to introduce the beam into the dipole.

The SC200 degrader consists of a half-wedge and two full wedges (20° wide) symmetrically distributed in the beam view, and Fig. 2a shows the schematic diagram.Energy reduction is directly correlated to the thickness of graphite (ρ = 1.842 g/cm3, I = 81 eV), and the location of the wedge inserted into the beamline can be obtained by a trigonometric function of its geometry. Polynomial fitting helps to obtain the calibration curve for the degraded energy-wedge thickness during commissioning. Graphite with a maximum thickness of 133.58 mm is allowed in the beam path to convert 200 MeV kinetic energy to 70 MeV at the exit of the degrader, resulting in the lowest transmission efficiency of 1.67% and 0.375% of the protons from the cyclotron reaching the exit of the Col4 and dipole.

The dose rates usually required for deep tumor treatment are a few Gy/min, which are readily available at high energies.Nevertheless,eye melanoma treatment requires a reasonably high intensity beam with low energies and short irradiation times [12]. Regarding the cyclotron-based proton therapy facility, improvement of the transmission efficiency in the degrader system is conducive to obtaining a sufficient dose rate.The design of the degrader should be considered from several aspects.

Fig. 1 (Color online) Schematic layout of the degrader and collimators in the SC200 facility. Rin for Clo2 and Rout for Col4 are 1.2 mm and 8 mm, respectively. The origin in the global coordinate system is the extraction reference point of the cyclotron, and the positive of Y is to the up looking in the direction of beam travel

Fig.2 (Color online)Specifications of multi-wedge geometry in the SC200 facility(a)and the new combined degrader structure(b).The origin of the local coordinate system is 137.5 mm upstream of the exit of the two degraders. The illustrated diagram is not to scale

(1) The mechanical transmission ratio, which is associated with the number and angle of wedges, affects the energy layer switch time and modulation range.

(2) Continuous energy regulation obtains a uniform Bragg peak.

(3) Take into account the engineering properties of the material, such as its machinability and outgassing rate under vacuum.

The new degrader structure is a combination of a double graphite wedge and B4C blocks (ρ = 2.52 g/cm3,I = 84.7 eV), and Fig. 2b shows the geometric configuration. The blocks are the initial energy adjustment unit for energy segmentation and move vertically to achieve different length settings or avoid the beam path completely.The wedge acts as the accurate regulation unit within each energy region.The reason for retaining part of the wedge is that it enables continuous modulation of the beam energy,which is necessary for fast beam scanning. Energy modulation is accomplished in segments by varying a double wedge thickness and the corresponding B4C length.

(1) Achieving a final energy final energy ＞160 MeV only uses wedge-shaped graphite for energy reduction.

(2) Deceleration to 110 - 160 MeV requires the insertion of a 39.3 mm B4C block behind the wedge.

(3) A 76 mm B4C is selected for simultaneous operation with a graphite wedge for energy modulation to ＜110 MeV.

2.2 Simulation settings and methods

Beam delivery simulation (BDSIM) is an effective particle-tracking program that utilizes the Geant4 toolkit to simulate the transport of particles and their interactions with materials.It is capable of constructing3D models of a variety of accelerators and magnets, as well as degraders,collimators and slits. These give it a unique ability to perform beam dynamics simulations in beamline models[13]. Conveniently, no additional magnetic field map need to be imported to achieve precise simulations of electromagnetic processes.Proper physical processes facilitate the detailed description of transport dynamics and nuclear reactions, which refer to the Geant4 documentation guide[14, 15]. The density of graphite can be defined by user code,while the mean ionization potential is consistent with the Geant4 material database. To explore the effect of a degraded beam on downstream transmission, we sample the beam properties at the exit of the first dipole in the energy select system with BDSIM (version 1.4). The magnet field of QE1 is set to - 5.525 kG, and set QE2 with 4.54 kG.

FLUKA Monte Carlo method is widely used in radiation protection calculations as it is consistently reliable over the entire energy range of particle projectiles, such as energy deposition, residual dose rates and shielding activation.Flair is an advanced visual interface that is the preferred way to input beam properties and establish geometries with specific materials [16-19]. To implement recording requirements, it is necessary to match the appropriate physical card. In this study, the physic cards of COALESCE and EVAPORAT needed to be activated for the scoring of residual nuclei.The proton interactions with two degraders are based on the FLUKA (version 4.1) and Flair(version 3.1-8).

Furthermore, each proton has a different energy loss owing to the influence of inelastic scattering. As the thickness of material inserted into the beam path increases,the interactions between protons and atomic nuclei are more frequent. The ionization loss of the beam tends to have a Gaussian probability distribution due to the reductions caused by random effects. On the contrary, the interaction frequency of protons decrease with a thin medium used for energy reduction. In this case, the influence of randomness increases and leads to statistical fluctuation. 106primary protons are run in the simulation to account for the reduction in statistical fluctuation. Table 1 lists the initial parameters of the beam phase space at the entrance of the degrader used in this work.

3 Results and discussion

3.1 Beamline transmission efficiency

In order to determine the influence of the degrader on the downstream beamline, collimators and magnets must maintain the same constraining effect. Assuming that the exit face for the combined degrader is still positioned 137.5 mm from the beam source, the graphite properties are consistent with the current used in the SC200 degrader.Figure 3 summarizes BDSIM results for the energythickness relationship and transmission efficiency in the two degraders. The graphite thickness required for160 - 200 MeV degradation shows no difference in both degraders.

Table 1 Beam parameters (1σ) at the degrader entrance used in BDSIM

At low degradation energies of 70 - 110 MeV, the combined degrader has a significant effect on the beam transmission efficiency at the dipole exit, with the efficiency increasing to 0.511% at 70 MeV and 2.137% at 110 MeV. Compared with the multi-wedge degrader, the improvements are 36.26% and 70.55%, respectively. This enhancement effect is sustained up to 160 MeV; in the energy range of 115 - 155 MeV, the efficiency is increased by 8.02 - 56.04%. However, the multi-wedge degrader shows higher efficiency at energies of 160 - 195 MeV,being about 6.88% - 13.85%more than that of the combined degrader.Due to the need for no more than 10 dynamic intensity ratios Imax(E)/Imin(E) during clinical treatment, additional measures are demanded to suppress beam currents at high energies in proton therapy applications [20]. This indicates that decreased transmission at higher energies is not a disadvantage;rather,there is a lower dependence of efficiency on the degraded beam energy.Another noteworthy issue related to the momentum distribution is that the increase in material thickness required for a beam path with low-energy transport leads to increased energy dispersion and considerable beam losses in the dipole.

The combined design allows the 200 MeV proton beam to be reduced to a minimum of about 42 MeV.The energy regulation process occurs entirely in the degrader with no need to install range shifters at the nozzle. This avoids the radiation risk the treatment of superficial tumors and better limits transverse divergence of the beam at the isocenter.Another advantage is that an appropriate increase in wedge angle shortens the response time of degrader.

3.2 Energy spread and transverse phase space

Charged particles passing through the degrader mainly experience multiple Coulomb scattering. It is the primary factor causing lateral beam divergence and emittance growth and positively correlated with reduced energy. The low-energy degradation usually creates a halo distribution that encircles the Gaussian peak in the transverse beam profile, and long tails in the lower and higher energy regions surround the main peak of the energy spectrum.Taking 70 MeV degradation as an example, Fig. 4 plots the proton horizontal coordinates (a) and energy distributions (b) followed by inelastic tails at the exit of the combined degrader.

Given that only Gaussian cores can pass through the collimator and dipole during actual transmission, we process the data of the transverse phase space and energy spread by removing the beam tail and limiting the analysis to beam core performance.That is,the sampled protons onthe detector are subjected to frequency analysis and Gaussian fitting. Combining the average and standard deviations σ (FWHM/2.355), the beam cores are obtained by the following constraints:

Fig.3 (Color online)Thickness settings with resulting energies(70 - 200 MeV)and corresponding transmission efficiency in the multi-wedge degrader (a) and combined degrader (b). The degradation step is 5 MeV

where i and i′are defined as the proton position and divergence in horizontal (x) or vertical (y) degraders for different energy reductions presented in Fig. 4c-e.

The influences of different degraders in the phase spaces follow similar trends as the changes in transmission distributions. Significant differences in emittance and beam spots are evident in the 70 - 110 MeV region. Compared to the multi-wedge degrader at 70 MeV setting, the emittance and the beam spot size of the combined degrader in the horizontal direction are reduced by 15.16% and 12.52%, respectively. Correspondingly, similar trends appear in the vertical direction, with decreases of 15.56%and 16.27%. The spatial divergence of the beam after leaving the combined degrader increases slightly at higher energies of 160 - 200 MeV. A reasonable explanation is that drifts exist both in front of and behind the combined degrader, where the distance of the degrader exit from the Col2 is 8 cm at 160 - 200 MeV.

For the protection of normal tissue at the posterior end of tumor, the dose gradient at the distal fall of the Bragg peak is usually required to be as steep as possible. The socalled distal dose fall-off (DDF) value (i.e., the distance from 80 to 20% position of the maximum dose) is mainly determined by energy spread of the incident beam and proton range straggling in a tumor. The latter always provides approximately 1.1% of the proton range to the DDF value, even at different energies [21]. Depending on the clinical requirement, momentum spread often drops to ±0.25% or ± 0.5% during ocular treatments. Since the inevitable range straggling of protons within a tumor is the prime reason for distal penumbra, ± 0.5% to ± 1% are acceptable in deep tumor treatments. A momentum slit upstream of the beamline can be used for this purpose.Hence,an increase in energy dispersion at the degrader exit will predict more beam loss in the slit.

As presented in Fig. 4e, although the two degraders have different materials and thicknesses,the energy spread under the same degradation energy setting is almost identical.Thus,the proportions of protons filtered in the slit are consistent. The results show that the energy dispersion is not influenced by the degrader properties and is dependent on the reduced energy, which is consistent with the research of Hsi [22].

3.3 Secondary particle spectra

As previously mentioned, in addition to Coulomb interactions between colliding nuclei, nuclear interactions lead to the release of nuclear fragments[23].The degrader and collimators are the main sources of secondary particle contamination. In particular, neutrons have no charge and their path remains unchanged by the deflect action of the dipole. Prolonged action on parts such as beam pipe seals and insulation may accelerate material deterioration. Figure 5 shows the simulated secondary particle spectra of two degraders under energy reduction from 200 to 70 MeV. A vacuum-filled spherical target is placed at the center of the degraders to sample the surrounding secondary particles.

Fig. 4 (Color online) Analysis of the horizontal position (a) and energy spectrum (b) used to distinguish the Gaussian core from the beam tail at a degrader setting of 70 MeV. The emittance (c), spot size (d) and energy spread (e) of the degraded beam at the exit of degraders at energy setting of 70 - 190 MeV (10 MeV steps)

The photons are emitted as the excited nuclei return to the ground state. They may interact with orbital electrons and transfer all their energy via the photoelectric effect or transfer part of it via Compton scattering. It can be observed in Fig. 5a that the maximum photon energy generated from nuclear interaction between protons and the degraders is both about 16 MeV, which is above the threshold of 1.022 MeV, and the photons reappear as positrons and electrons. Besides, Fig. 5b shows that the maximum secondary neutron energy produced by the degraders is both around 180 MeV,and the yield decreases with increases in energy.Most of the energies produced are within 20 MeV, which are the boundary between fast and relativistic neutrons. The energy of fast neutrons gradually decreases through elastic or inelastic collisions with other nuclei until they are reduced to thermal neutrons or are captured.

Fig.5 (Color online)Energy spectral of electrons and photons(a),neutrons(b)generated by the combined degrader and multi-wedge degrader.The initial kinetic energy of 200 MeV is deaccelerated to 70 MeV

Although the energy spectral distributions of the combined and multi-wedge degraders are similar,the secondary particle yields of the combined one are slightly higher because of the larger nuclear interaction cross section of boron. Due to the relatively long range of neutrons, the main considerations in radiation shielding for the degrader are the deceleration and absorption of neutrons. Hence,additional work is needed to assess the adequacy of the concrete shielding in the degrader region.

3.4 Activation

Locations with heavy beam losses are predictive of high radiation levels.To minimize the personal dose received by maintenance staff, low activation is an important consideration when selecting the degrader material. The degraders were both set for 70 MeV degradation with a 400 nA beam intensity extracted from the cyclotron for a 1 h irradiation period. The radionuclides created in the degraders are listed in Table 2 for different cooling time intervals.The assumed volumes of the materials are 161.25 cm3for the multi-wedge degrader, and 58.05 cm3and 76 cm3for the graphite and B4C, respectively, used in the combined degrader.

A total of 20 radioisotopes are produced instantly at the end of 1 h of irradiation. The most important cooling time is 1 h, as 65% of the isotopes decay to 0 at that time. The dominant contributors to the total activity at this moment are11C and7Be,which produce about twice the activity in the multi-wedge degrader as in the combined degrader. A comparison between cooling times of 1 h and 1 day shows no significant changes in the activity of the remaining radionuclides due to their long half-lives, except for sharp decreases in11C and13N. Approximately 99.79% of the11C release β ＋and decay to11B, which is accompanied by the production of positrons that are annihilated with electrons to create photons[24].The decay process of13N is similar but with a shorter half-life of 10 min and is about half that of11C. The isotopes that have higher activity in the combined degrader than in the multi-wedge one are3H and10Be, which only decay by emitting β- and make a negligible contribution to the personal dose due to their low activity.In addition, the decay process of7Be involves the emission of γ and implies a lower individual γ-dose rate than with the multi-wedge degrader. Maintenance and replacement of the ion source inside the cyclotron are performed every two weeks, and the nearby degrader will complicate the operation. However, maintenance work is not interrupted by the incomplete decay of isotopes. The discussion also highlights the need for radiation protection from β and γ doses.

Table 2 The activity level at several moments for combined and multi-wedge degraders (unit: Bq)

3.5 Radiation

Ionizing radiation from inelastic collisions between the proton beam and material atoms is the main source of prompt radiation in the degrader. In this section, we describe the ambient dose equivalent rates at lateral distances within 2 m after 1 h of irradiation. For induced radiation generated from radioactive residual nuclei, the activity levels are evaluated after irradiation stops.According to the univariate method, simulations only consider the impacts of the degrader materials on doses,while excluding auxiliary components such as the mechanical support, vacuum chamber and seals. Table 3 compares the equivalent dose rates obtained from degraders immediately after shutdown and after various cooling times, both corresponding to maximum degradation settings of 200 MeV to 70 MeV.Figure 6 shows the dose rate distributions on a horizontal plane within 1 m of the degraders after 3 h of cooling.

As shown in Fig. 6, the dose rate distribution dissipates outward with distance from the center of the degrader materials on the horizontal plane, with the highest dose occurring at the entrance of the wedge. Compared with prompt radiation results in Table 3, the dose rates around both degraders decrease by 1 and 3 orders of magnitude after 1 h and 3 h of cooling,respectively.After cooling for 1 day,there is no significant reduction in the ambient dose compared to that of 12 h, because the remaining induced radiation is formed from radioactive nuclei with longer half-lives.

The calculations show that both the prompt and induced radiation levels generated from the multi-wedge degrader are higher than those of the combined one.At 1 h and 24 h after system shutdown, the average dose rates on the horizontal plane around the multi-wedge degrader are 2 and 1.25 times higher, respectively, than those around the combined degrader. The results match the calculated activity results in Sect. 3.4.

4 Conclusion

The contribution performs detailed calculations to explore the feasibility of a new design of combined degrader for proton therapy. The degrader’s geometry consists of a double graphite wedge and B4C blocks of different lengths. The scheme incorporates the advantages of the compact structure of a segmented degrader and the continuous energy regulation of multi-wedge degrader.Moreover, the B4C block design solves the challenge of machining wedge shapes from a high-hardness material.

On this basis, we establish beam dynamics models in BDSIM, and two degrader models are extended to the downstream beamline through simulations of the particlematter interaction processes. The different beam characteristics of the degraders are investigated, mainly in terms of phase space and transport efficiency. The simulations show that the combined degrader can effectively improve the transmission efficiency in the 70-160 MeV energy range but slightly restrains the beam transport in the 160-200 MeV. For instance, the horizontal emittance (1σ)at the exit of the combined degrader decreases by 15.16%at a 70 MeV degradation setting. At the same time, the transmission through the first dipole in the energy select system is 36.26% higher than that of the multi-wedge degrader. However, at the 185 MeV setting, the transmission efficiency is reduced by 10.57%, which is beneficial for intensity suppression during high-energy treatments.

Further, beam losses in the degrader cause component activation, ambient irradiation and, even worse, secondary radiation that persists after system shutdown. Sincecyclotron maintenance usually starts 1-2 h after irradiation is stopped, we also focus on the dose equivalent and isotopic activation based on the FLUKA program.The results demonstrate that although the combined degrader produces more secondary particles due to the presence of boron, the radionuclide activity and radiation dose rate on the surrounding horizontal plane are both 50% lower after 1 h of cooling time than those of the currently used multi-wedge degrader.

Table 3 Maximum, minimum and average of ambient dose equivalent rates in horizontal plane within the range of 2 m around degraders (unit: pSv/s)

Fig. 6 (Color online) Ambient dose equivalent rate at 1 m around the multi-wedge degrader (a) and combined degrader (b) after 3 h cooling,and corresponding dose rates after 24 h of cooling (b) and (d)

Comprehensive comparisons indicate that the combined degrader has clear advantages in transmission and radiation.Meanwhile,the wider energy modulation range of the combined degrader,capable of reaching a minimum energy of 42 MeV, is particularly suitable for the treatment of superficial tumors without requiring additional range shifters to be mounted,thus resulting in less neutron radiation.Although the properties of combined degrader have been demonstrated in this paper, further experimental validations are needed to ensure medical utilization for the proton facility.

Author contributionsAll authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Man-Fen Han, Jin-Xing Zheng and Xian-Hu Zeng.The first draft of the manuscript was written by Man-Fen Han,and all authors commented on previous versions of the manuscript.All authors read and approved the final manuscript.