Physical and biological impacts of collimator‐scattered protons in spot‐scanning proton therapy

Abstract To improve the penumbra of low‐energy beams used in spot‐scanning proton therapy, various collimation systems have been proposed and used in clinics. In this paper, focused on patient‐specific brass collimators, the collimator‐scattered protons' physical and biological effects were investigated. The Geant4 Monte Carlo code was used to model the collimators mounted on the scanning nozzle of the Hokkaido University Hospital. A systematic survey was performed in water phantom with various‐sized rectangular targets; range (5–20 cm), spread‐out Bragg peak (SOBP) (5–10 cm), and field size (2 × 2–16 × 16 cm2). It revealed that both the range and SOBP dependences of the physical dose increase had similar trends to passive scattering methods, that is, it increased largely with the range and slightly with the SOBP. The physical impact was maximized at the surface (3%–22% for the tested geometries) and decreased with depth. In contrast, the field size (FS) dependence differed from that observed in passive scattering: the increase was high for both small and large FSs. This may be attributed to the different phase‐space shapes at the target boundary between the two dose delivery methods. Next, the biological impact was estimated based on the increase in dose‐averaged linear energy transfer (LET d) and relative biological effectiveness (RBE). The LET d of the collimator‐scattered protons were several keV/μm higher than that of unscattered ones; however, since this large increase was observed only at the positions receiving a small scattered dose, the overall LET d increase was negligible. As a consequence, the RBE increase did not exceed 0.05. Finally, the effects on patient geometries were estimated by testing two patient plans, and a negligible RBE increase (0.9% at most in the critical organs at surface) was observed in both cases. Therefore, the impact of collimator‐scattered protons is almost entirely attributed to the physical dose increase, while the RBE increase is negligible.


| INTRODUCTION
Most newly built proton therapy centers worldwide are implementing the pencil beam scanning (PBS) technique because of its distinct advantages of dose conformity to targets and neutron exposure reduction compared to the more conventional passive scattering methods. However, when shallow tumors are involved, the large spot size of the low-energy proton beam resulting from the large-angle Coulomb scattering might offset the dose conformity advantage gained by the scanning approach. 1 To overcome this problem, different collimators have been designed and increasingly used in the clinics [2][3][4] and their clinical benefits have been investigated in various studies, with positive results. 5 So far, most of the analytical dose calculation engines installed in the PBS treatment planning systems (TPSs) assume the collimator absorbs all the incident protons; that is, they neglect the dose contamination from the protons scattered by the collimator edge, while several studies have proven it could have a considerable dosimetric impact in reality. Van Luijk et al. 6 used a 160-MeV proton beam to measure and simulate scatter protons for a small field (<2 cm), showing that this contribution can be up to 20% at the patient surface. Titt et al. 7

conducted a systematic
Monte Carlo study with various target sizes and depths used in the clinics; they also suggested there is contamination from scattered protons.
However, both studies focused on the scattering approach and did not systematically investigate the collimators used in PBS.
Collimator-scattered protons can have an additional biological impact. The protons lose energy when hitting the collimator, and their linear energy transfer (LET) increases accordingly. A higher proton LET generates a greater biological effect, as observed in both in vivo and in vitro experiments [8][9][10][11][12] and even in the clinical outcome. 13 In the previously mentioned study, van Luijk et al. 6 estimated the increase of the biological damage based on a simple assumption that the protons with energy above 40 MeV have a relative biological effectiveness (RBE) of 1, while for those below 40 MeV have RBE of 1.2. In their experimental setup, only 5% of protons have the energy below 40 MeV at just below the collimator, implying that the biological damage to tissues would be at most 1% larger than that expected from the physical dose. Followed by the recent rapid progress of biophysical RBE models, 8,14 it may be interesting to revisit the biological impact of scattered protons.
In this study, we investigated the physical and biological impacts of the collimator-scattered protons used in the PBS system of the Hokkaido University Hospital. We systematically evaluated the effects of the collimator-scattered protons on the physical dose, the dose-averaged LET (LET d ), and the RBE. To evaluate the effects in real clinical settings, we simulated two patient plans. Finally, the difference between the PBS and passive scattering systems were discussed.

2.A | Beam collimation system for the spot-scanning beamline
The beam collimation system used for the spot-scanning beamline simulated in this study was an extrapolation of a short-range applicator (SRA) investigated by Yasui et al. 3 and consisted of a 2-or 4-cm thick brass collimator and a 4-cm thick energy absorber made of acrylonitrile-butadiene-styrene (ABS) plastic (Fig. 1). In the following paragraphs, it will be referred to simply as SRA. It was mounted at the most downstream portion of the gantry, with the lower surface of the collimator placed at 9 cm from the isocenter, and designed to have a maximum uniform field of 20 × 20 cm 2 at the isocenter. When using the configuration with the 2-cm thick collimator, the minimum and maximum available proton ranges after passing through a 4-cm thick energy absorber were 0.5 cm (74.9 MeV) and 10 cm (142.5 MeV) in water, respectively, and the in-air spot size at the isocenter ranged from 11.7 to 6.0 mm (one sigma). When using the 4-cm thick collimator, the minimum and maximum proton ranges were 0.5 cm (74.9 MeV) and 20 cm (192.4 MeV) in water, respectively, and the inair spot size ranged from 11.7 to 5.3 mm (one sigma).

2.B.2 | Target geometry
To systematically investigate the physical dose and RBE increase caused by the collimator-scattered protons, the simulation was performed for different target geometries in a water tank, and their parameters are summarized in Table 1   physical dose to the target was 2 Gy. The collimator opening size was set so to cover the edge of the proximal front of the targets with 50% of the prescribed dose.

2.B.3 | Physical dose and LET d calculations
The physical dose and LET d distributions were computed for collimator-scattered protons, unscattered protons, and both together. In the dose computation, the energy within each voxel was scored at each step for all particles and events, and the total sum was converted into the physical dose. In the LET d computation, the primary, secondary, and higher order protons were included, while the hadrons, leptons, and neutral particles generated via nuclear reactions were excluded. 17 This was primarily because the estimated contributions of these other particles to the dose are much smaller than the protons (<1%), and they have large uncertainties for the dependence of biological parameters, that is, α and β, on LET d . 17 For the computation of LET d using Geant4, it has been discussed that the value changes among different scoring techniques, as well as the tracking step size limit. [18][19][20] In this study, we followed Cortés-Giraldo et al. 20 and used the following equation for computing LET d : where n is the event index, S n indicates the steps taken by the primary and secondary protons in the voxel for the n-th event, and ε sn and L sn are the energy deposited by proton and the mean energy loss per unit path length along the s-th step in the n-th event, respectively. To compute L sn , the ComputeElectronicDEDX() function of the G4EmCalculator class was used. 15 From now on, the physical dose and LET d originated from the collimator-scattered protons will be referred to as D S and ¼ πr 2 LET S d , respectively, while those resulting from the unscattered protons and all protons (scattered + unscattered) will be indicated by the superscripts US and S + US, respectively.

2.C | RBE calculation
The RBE was calculated using the linear-quadratic (LQ)-based RBE model developed by McNamara et al. 22 : where D is the physical dose, and α and β are the LQ parameters for the reference x-ray radiation. The LET d dependence is implicit in RBE max and RBE min :

2.D | Evaluation
The z-axis was the selected incident beam direction and its origin, z = 0, was located at the water surface; x and y were the transverse coordinates. We considered z s = 5 mm as the representative normal tissue depth at the surface and z c as the target center depth. The xposition receiving the maximum dose by the collimator-scattered protons at z s was defined as x s In this study, α/β was set to 10 Gy at the target center and to 3 Gy at z s . 22 Note that these values fit for only some of the tumor sites. For the α/β parameter, a wide range of heterogeneity has been observed among tumor sites. In addition, recent literature review has revealed that the study heterogeneity for example, tumor stage, type of biological models and clinical endpoints gives large variation in the α/β parameter even for the same tumor site. 23 The following parameters were evaluated for all the target geometries; 1. The maximum physical dose deposited by the collimator-scat- 3. The relative biological effectiveness of the unscattered and all protons at (x s ,0,z s ), that is, RBE US (x s ,0,z s ) and RBE S+US (x s ,0,z s ), and at the target center, that is, RBE US (0,0,z c ) and RBE S+US (0,0,z c ).

2.E | Patient treatment plan
Two simulated cases (Case A: ocular melanoma, Case B: childhood rhabdomyosarcoma) for which the collimator is beneficial to spare the surrounding normal organs were considered (Fig. 3). The treatment plan was created with the VQA TPS (Hitachi Ltd., Tokyo).
A pencil beam algorithm, in which the lateral fluence profile is modeled as a double-Gaussian function, 24,25 was used. The spot decomposition method was used to account for tissue heterogeneity and the collimator boundary across the beam's cross-section. 26,27 The prescriptions were given to D99 and D50 of the clinical target volume (CTV), respectively, assuming that the RBE had a constant value of 1.1. The CTV size, range and FS of the targets, and the prescription per field are summarized in Table 2. The single field was used in both plans, and a 5-mm collimator margin was selected to cover the CTV with the prescribed dose.
We     At the target center, the maximum scattered dose does not exceed 2.6% over all tested conditions, as shown in Fig. 6(b). It is largest with a small FS because of the largest overlap from the four collimator walls; for small FSs, the scatter dose decreases with the range because the scattered protons stop before reaching the target center.  Figure 7(b) shows the same quantities as Fig. 7(a) at the target centers. In this case, the collimator-scattered dose is as small as shown in Fig. 6(b) Table 1, normalized by the physical dose from the unscattered protons at the target center.
| 53 magnitude of RBE increase is not significant because its maximum is only 0.04. 3.E | Physical dose, LET d , and RBE increase with the patient geometry ) at a 5-mm depth and at the xposition receiving the maximum scattered dose from the collimator (a) and at the target center (b) for the various target geometries listed in Table 2. RBE was observed in both cases, regardless of the α/β values (10 and 3 Gy).

| DISCUSSION
We investigated the physical and biological impacts of collimatorscattered protons used in a PBS system. In their pioneering work, van Luijk et al. 6 focused on very small field sizes (up to 2 × 2 cm 2 ), while this work was a systematic survey of FS up to 16 × 16 cm 2 , which covers a wider range of tumor sites and is almost the same size as that investigated by Titt et al. 7 In the passive scattering, the impact of collimator scattering rapidly decreases as the FS increases from 3 × 3 to 10 × 10 cm 2 and does not change from 10 × 10 to 15 × 15 cm 2 (see Fig. 4 in Titt et al. 7 ). We found that, in contrast to the passive scattering, the impact becomes large not only at small, but also large FSs, and this was attributed to the difference in proton beams' directionality between PBS and passive scattering. In passive scattering, the beam angle has a little correlation with the distance from the beam axis but, in PBS, the beam has a finite angle that is proportional to the lateral displacement with respect to the beam central axis. Since the X and Y scanning magnets are placed at different positions, the impact size is different among the scanned directions. Aside from the FS dependence, the physical dose impact by collimator-scattered protons observed in this research is consistent (or, at least, is not in contrast) with the research of Titt et al. 7 In both studies, the physical dose impact increases with the range at the water surface, according to the increased number of protons passing through the collimator; at the target center, the impact is comparable between different ranges and weakly increases with SOBP.
To the best of our knowledge, this is the first study of the biological impact of collimator-scattered protons using the LQ-based LET-dependent RBE model. In both water surface and target center depth, the LET S d is highest at the field center and can exceed 10 keV/μm. However, the scatter dose is not large enough to increase the total LET d by 1.0 keV/μm. Although we have reported results for only limited positions in each geometry, this is true for all the positions and geometries receiving a dose >0.3 Gy (15% of that at the target center). Figure 9 shows the scatter plot for the LET d F I G . 8. Relative biological effectiveness from the unscattered (RBE US ) and the scattered + unscattered protons (RBE S+US ) for the various target geometries listed in Table 2, at a 5-mm depth, and at the xposition receiving the maximum dose (α/β = 3 Gy) (a) and at the target center (α/β = 10 Gy) (b).
increase (LET SþUS d − LET US d ) against the D S increase for the target R15_FS8_S5: all the voxels receiving a D S above 0.01 Gy are plotted.
In general, an LET d increase greater than 1 keV/μm is observed only in the voxels receiving small D S (<0.08 Gy, that is, 4% dose of the prescription); in those receiving a large D S (>0.08 Gy), instead, there is only a small increase (<1 keV/μm). This indicates that the enhanced LET S d does not affect the total LET d , not only at the water surface and target center depth but at all positions.
One of the limitations of this work is that the number of scattered protons at the target center was not large enough to have statistically meaningful results. The large LET S d variations observed for several geometries in Fig. 7 21 Due to the large variation in the RBE estimates because of the fundamental differences in experimental databases, model assumptions, and regression techniques, 29 we estimated the model dependence of our results using two other models. 30,31 Different RBE models give different RBE; however, in both models, the magnitude of RBE increase is not significant (lower than 0.03 and 0.06 at the water surface and 0.003 and 0.005 at the target center, respectively).
The patient plan simulation results are almost consistent with the rectangular targets in the water phantom. However, due to the large variations of collimator shape and OAR location, the physical dose increase must be assessed patient-by-patient. Several analytical approaches have been proposed for passive scattering in the past 28,32,33  In this study, a patient-specific collimator was used to effectively create a sharp penumbra along the outermost contour of the target.
As an alternative, apertures that can adapt their shapes energy layerby-energy layer have been developed, 2,4 but they may suffer from a greater collimator scattering in return for the increased conformity, which could be the subject of future investigations.

| CONCLUSION S
Both the physical and biological impacts of the collimator-scattered protons used in PBS proton therapy were studied. Monte Carlo simulations revealed that a non-negligible amount of physical dose was contaminated by the collimator scattering (3.0%-22.0% at the surface). The observed behavior was similar (or, at least, not contradictory) to previous research about the range and SOBP dependence in passive scattering. On the other hand, a different behavior was observed in terms of FS between PBS and passive scattering. The collimator-scattered protons exhibited LET d up to 6.6 times greater than the unscattered ones. However, when averaged by dose, the total LET d was barely increased compared to the unscattered protons. Therefore, increased biological impact by the collimator-scattered protons can be almost entirely attributed to an increased physical dose and not to the increase in RBE due to the LET d increase.
Yu Hiyama for their valuable support. This research was supported by JSPS KAKENHI Grant No. 18K07621 and the "Global Institution for Collaborative Research and Education (GI-CoRE), Hokkaido University", founded by the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

CONFLI CT OF INTERESTS
We disclose that Shusuke Hirayama received funds from Hitachi, Ltd., Tokyo, Japan. F I G . 9. The increase in dose-averaged linear energy transfer (LET d ) against the increases in physical dose from the collimator-scattered protons (D S ) for the target R15_FS8_S5, based on the voxels receiving more than 0.01 Gy.