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Published in final edited form as: Phys Med Biol. 2024 Jan 17;69(3):10.1088/1361-6560/ad0b64. doi: 10.1088/1361-6560/ad0b64

Modelling small block aperture in an in-house developed GPU-accelerated Monte Carlo-based dose engine for pencil beam scanning proton therapy

Hongying Feng 1,2,3, Jason M Holmes 2, Sujay A Vora 2, Joshua B Stoker 2, Martin Bues 2, William W Wong 2, Terence S Sio 2, Robert L Foote 4, Samir H Patel 2, Jiajian Shen 2, Wei Liu 2,*
PMCID: PMC11009986  NIHMSID: NIHMS1983234  PMID: 37944480

Abstract

Purpose.

To enhance an in-house graphic-processing-unit accelerated virtual particle (VP)-based Monte Carlo (MC) proton dose engine (VPMC) to model aperture blocks in both dose calculation and optimization for pencil beam scanning proton therapy (PBSPT)-based stereotactic radiosurgery (SRS).

Methods and materials.

A module to simulate VPs passing through patient-specific aperture blocks was developed and integrated in VPMC based on simulation results of realistic particles (primary protons and their secondaries). To validate the aperture block module, VPMC was first validated by an opensource MC code, MCsquare, in eight water phantom simulations with 3 cm thick brass apertures: four were with aperture openings of 1, 2, 3, and 4 cm without a range shifter, while the other four were with same aperture opening configurations with a range shifter of 45 mm water equivalent thickness. Then, VPMC was benchmarked with MCsquare and RayStation MC for 10 patients with small targets (average volume 8.4 c.c. with range of 0.4–43.3 c.c.). Finally, 3 typical patients were selected for robust optimization with aperture blocks using VPMC.

Results.

In the water phantoms, 3D gamma passing rate (2%/2 mm/10%) between VPMC and MCsquare was 99.71 ± 0.23%. In the patient geometries, 3D gamma passing rates (3%/2 mm/10%) between VPMC/MCsquare and RayStation MC were 97.79 ± 2.21%/97.78 ± 1.97%, respectively. Meanwhile, the calculation time was drastically decreased from 112.45 ± 114.08 s (MCsquare) to 8.20 ± 6.42 s (VPMC) with the same statistical uncertainties of ~0.5%. The robustly optimized plans met all the dose–volume-constraints (DVCs) for the targets and OARs per our institutional protocols. The mean calculation time for 13 influence matrices in robust optimization by VPMC was 41.6 s and the subsequent on-the-fly ‘trial-and-error’ optimization procedure took only 71.4 s on average for the selected three patients.

Conclusion.

VPMC has been successfully enhanced to model aperture blocks in dose calculation and optimization for the PBSPT-based SRS.

Keywords: Monte-Carlo dose engine, pencil beam scanning proton therapy, block aperture, stereotactic radiosurgery

1. Introduction

Stereotactic radiosurgery (SRS) is commonly used for primary and metastatic brain tumors (Yamamoto et al 2014, Milano et al 2021). The conformal and compact dose distributions from SRS allows for sparing of the adjacent normal tissues with anatomical complexity in brain. Conventional SRS was first proposed and continuously developed with photon therapy. Compared to photon therapy, proton therapy has the intrinsic geometrical sparing characteristic i.e. a proton beam deposits all of its energy within a certain range and none beyond, known as the Bragg-peak (Frank et al 2014, Schild et al 2014). Previously, proton-based SRS was proposed using the passive scattering (PS) delivery technique (Halasz et al 2011, Atkins et al 2018). With the development of the pencil beam scanning (PBS) delivery technique (Pflugfelder et al 2008, Unkelbach et al 2009, Fredriksson et al 2011, Liu et al 2012a, 2012b, Liu et al 2016, Shan et al 2018, Liu et al 2020, Feng et al 2021a, 2021b), the PBS proton therapy (PBSPT) can achieve an optimal dose distribution with superior target dose conformity and adjacent organs-at-risk (OAR) sparing. A few exploratory investigations (Amelio et al 2019, Fellin et al 2019, Bussiere et al 2021) on the PBSPT-based SRS have been conducted to pursue superior dosimetric outcomes.

Due to the beamlet level flexibility, the use of patient-specific apertures is largely eliminated in PBSPT compared to PS proton therapy, leaving the lateral fall-off of a dose distribution dominantly determined by the spot size (σ) of individual beamlets. Modern PBSPT systems worldwide mostly have small spot sizes. However, brain tumors at shallow locations necessitate the use of range shifters to pull back the Bragg-peaks of proton beams. Consequently, beamlets undergo additional Coulomb scattering due to the range shifter, resulting in enlarged spot sizes possibly exceeding 15 mm (Shen et al 2015, 2016, 2017a, 2017b). With larger spot sizes, the lateral dose fall-off impairs the sparing of adjacent OARs (van de Water et al 2012, Wang et al 2014). To address this issue, a patient-specific aperture was proposed in PBSPT (Dowdell et al 2012, Yasui et al 2015, Moteabbed et al 2016, Bäumer et al 2019, Rana et al 2021).

When an aperture is present in the field, the edge-scattered protons will introduce additional perturbations and possible contaminations (Titt et al 2008, Bäumer et al 2019) in the resulting dose distribution. Such contaminations are not well modelled by analytical dose calculation algorithms (Zhao et al 2015, Holmes et al 2022a, 2022b), which may lead to unexpected clinical results (Widesott et al 2018). Therefore, Monte Carlo (MC)-based proton dose engines are more preferred to accurately model the apertures. RayStation MC (RaySearch Laboratories AB, Stockholm, Sweden) supports MC-based modelling of aperture blocks (Bäumer et al 2019, Maes et al 2019). However, the ‘voxelization’ method used for modelling the aperture opening within RayStation MC may become problematic when the aperture opening is small (Holmes et al 2022b). In a recent study (Holmes et al 2022b), an independent open-source fast MC proton dose engine, MCsquare (Souris et al 2016), was enhanced to model patient-specific aperture blocks with openings as small as 1 cm across, where the aperture openings were better modelled by directly connecting the aperture opening boundary points. The precision of the enhanced MCsquare was validated to be adequate for the use of dose calculations. However, considering that PBSPT is very sensitive to various uncertainties such as patient setup uncertainty and proton range uncertainty (Unkelbach et al 2018), robust optimization has been proposed to mitigate the impact of these uncertainties (Pflugfelder et al 2008, Unkelbach et al 2009, Fredriksson et al 2011, Liu et al 2012a, 2012b, Liu et al 2016, Shan et al 2018, Liu et al 2020, Feng et al 2021a, 2021b), which requires far more computation than conventional optimization. The calculation speed of the enhanced MCsquare was not fast enough for robust optimizations in PBSPT treatment planning.

To achieve fast and accurate MC-based robust optimization for PBSPT, a graphic processing unit (GPU)-accelerated MC dose calculation engine based on the newly proposed novel concept of virtual particles (henceforth referred as virtual particle Monte Carlo or VPMC) was developed recently (Shan et al 2022). In this study, our aim was to enhance VPMC to model aperture blocks in both dose calculation and robust optimization for the PBSPT-based SRS treatment planning.

2. Materials and methods

2.1. Modelling aperture blocks

Virtual particle (VP) is a statistical concept that works by converting the histories of realistic particles (i.e. primary and secondary protons with further simplifications) to the histories of VPs, in terms of particle transport and energy deposit. Please refer to Shan et al (2022). for more details of the VP concept and the implementation of the VPMC proton dose engine.

The aperture block is a brass block of 30 mm thickness with a patient-specific opening. The brass block with such thickness is capable of blocking protons with energy as large as about 155 MeV, which exceeds the energies clinically used for the treatment of shallow brain cancers. Dedicated applicators for proton SRS were designed, which attaches to the proton nozzle and can hold brass apertures to collimate proton beam by extending the downstream face of the aperture at 150 mm to isocenter (Shen et al 2023). To treat shallow tumors, a circular ABS Resin with 6.1 cm diameter and water equivalent thickness (WET) of 45 mm can be placed upstream against the brass aperture to work as a range shifter (Shen et al 2015) with its downstream face at 190 mm to isocenter (therefore a 10 mm gap between the range shifter and the aperture block, figure 1(a)).

Figure 1.

Figure 1.

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Aperture block and range shifter configurations at our institution and aperture block w/ and w/o range shifter configurations used in the water phantom validation. (a) Aperture block and range shifter configurations in PBSPT-based SRS. (b) Configurations of the aperture block without range shifters in ConfigA. (c) Configurations of the aperture block with a range shifter in ConfigB.

Similar to the range shifter implementation in the original VPMC (Shan et al 2022), the aperture block was incorporated into VPMC using the same methodology except for a few aperture-specific arrangements as follows. To account for the aperture block material in VPMC, a brass phantom was used to generate the aperture block-related physics parameter probability distribution functions (PDFs). The so-called crossing number algorithm (Shimrat 1962) was used to determine whether the VP was in the opening or brass block for each MC simulation step. If the VP was in the opening, it would simply be transported with the previous velocity and direction. If the VP was in the brass block, the status of the VP would be updated according to the physics parameters sampled from the pre-generated aperture block-related physics parameter PDFs. The newly enhanced VPMC, capable of modelling apertures, was then integrated in a previously developed in-house TPS, named Shiva (Shan et al 2020, Yang et al 2021, Feng et al 2021a, 2021b, Feng et al 2022, Yang et al 2022).

2.2. Validation of the aperture modelling

The aperture modelling was validated by comparing the calculated results with MCsquare and RayStation MC in the following three experimental setups. First, single proton beamlets of various energies were delivered to a homogenous water phantom. Second, a single energy layer composed of many proton beamlets was delivered to the homogenous water phantom. Third, treatment plan doses were calculated in patient geometries with inhomogeneities considered. Please note that all the aperture blocks used in this study were non-divergent aperture blocks.

Please note that MCsquare has been thoroughly validated against other MC codes and measurements in both phantoms and patient geometries (Souris et al 2016, Sorriaux et al 2017, Huang et al 2018, Deng et al 2020, Wagenaar et al 2020, Holmes et al 2022a, 2022b). In addition, MCsquare has been fully commissioned and incorporated into clinical workflows to serve as the second monitor unit (MU) check system at a few proton centers for years (Deng et al 2020, Liu et al 2021, Holmes et al 2022b). More importantly, MCsquare has been enhanced to model the aperture block and validated with measurements and RayStation MC (Holmes et al 2022b). Therefore, we may safely assume that the aperture enhanced MCsquare is a good anchor for the development and validation of aperture enhanced VPMC in terms of accuracy.

2.2.1. Single beamlet validation in water phantom

There were two machines involved in the PBSPT-based SRS with an aperture block, as shown in figure 1(a), the one with a range shifter (APRS) and the other without a range shifter (AP). For both AP and APRS machines, 97 proton energies used in our proton machines were used ranging from 71.3 to 228.8 MeV. The aperture block opening was 1 cm for both machines. In the validation, all beamlets used were delivered along the beam axis direction with the same lateral location, i.e. at the boundary of the aperture block opening to consider the influence of the aperture block upon the dose of the beamlets.

For every energy used in both machines, two simulations were conducted by two different dose engines for comparison, VPMC and MCsquare, respectively. The number of particles to be simulated (VP in VPMC and primary proton in MCsquare) were appropriately selected to achieve <0.5% and comparable statistical uncertainties for both dose engines (Shan et al 2022). The dose grid resolution used in simulations was 1 mm in all three cardinal directions. The dose distributions calculated by VPMC and MCsquare were compared in pairs through 3D gamma analysis (Low et al 1998) with a criterion of 2%/2 mm and a threshold of 10%.

2.2.2. Energy layer validation in water phantom

Figures 1(b), (c) show the validations in water phantoms, using two different configurations (henceforth referred as ConfigA and ConfigB). In ConfigA (figure 1(b)), the isocenter was 108 mm below the water surface. Proton beamlets of 147.0 MeV were applied along the beam axis direction through an aperture block of 30 mm thickness that was mounted by the Hitachi holder aligned to the beam central axis with its distal surface 15 mm upstream the isocenter. Four aperture blocks were used with ascending central opening of 1, 2, 3, and 4 cm. In ConfigB (figure 1(c)), a few modifications were made compared to ConfigA: (1) a range shifter of 45 mm WET was introduced along the beam central axis and upstream the aperture block with its distal surface 190 mm upstream the isocenter (thus there is a 10 mm gap between the aperture block and the range shifter), (2) the beamlet energy was elevated from 147.0 to 161.5 MeV. For both configurations, the mono-energetic proton beamlets were set to have the same intensity and were uniformly distributed in a square pattern with a spot spacing of 2.5 mm to cover the entire opening and the associated 5 mm outer margin (i.e. forming a circular irradiation field).

For each simulation scenario (4 in both ConfigA and ConfigB), similar calculations and comparisons were done as in the previous subsection ‘Single Beamlet Validation in Water Phantom’.

2.2.3. Treatment plan validation in patient geometries

Ten brain cancer patients with small and shallow clinical target volumes (CTVs) previously treated using the photon SRS or stereotactic body radiotherapy (SBRT) technique at our institution were selected to validate the enhanced VPMC in patient geometries with inhomogeneities considered. Proton SRS treatment plans were first generated for these 10 patients in RayStation using its fast MC dose engine and then forward dose calculations of the generated plans were done using VPMC and MCsquare. The proton treatment plan information of these 10 patients is listed in table 1. All of the MC calculations performed by VPMC, MCsquare and RayStation MC achieved a low statistical uncertainty of <0.5% with a dose calculation resolution of 2 mm in all three cardinal directions, according to the recommendation from AAPM Task Group 101 (Benedict et al 2010). The dose distributions calculated by VPMC and MCsquare were compared to the dose distributions calculated by RayStation MC using 3D gamma analysis with criteria of 3%/3 mm, 3%/2 mm, and 2%/2 mm, respectively, and a threshold of 10% (table 2). The 3D gamma pasting rates from VPMC and MCsquare were statistical compared using the Wilcoxon signed-rank test to get the statistical significance. A p-value<0.05 is considered to be statistically significant. The calculation time of each plan by VPMC and MCsquare were also recorded and compared.

Table 1.

Treatment planning information of the 10 selected patients.

Patient # Prescription dose (Gy [RBE]) Number of fractions CTV volume (c.c.) Treatment field angle Range shifter Block effective diameter (cm)
1 38 5 3.3 T180G80a No 2.4
T0G123 No 2.4
T180G90 Yes 2.4
2 27 3 4.1 T180G65 Yes 2.5
T180G90 Yes 2.6
3 20 1 4.5 T180G120 Yes 2.9
4 20 1 6.7 T0G70 Yes 2.7
5 20 1 0.4 T180G90 No 1.8
T0G90 No 1.8
6 25 5 10.2 T180G45 Yes 3.6
T180G90 Yes 3.4
T180G180 No 3.6
7 39 5 7.4 T180G180 Yes 3.0
8 12 1 43.3 T250G90 No 5.2
T310G70 No 5.1
T0G105 No 5.2
T270G355 No 4.6
9 24 3 1.3 T180G80 Yes 1.8
10 16 1 2.6 T180G160 Yes 2.6
T0G160 Yes 2.6
Mean — — 8.38 — — 3.11
SD — — 12.62 — — 1.11
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abbreviations: CTV for clinical target volume, SD for standard deviation, RBE for relative biological effectiveness.

a

T for table and G for gantry.

Table 2.

3D gamma passing rates (%) of treatment plan dose validation in patient geometries by comparing MCsquare and VPMC with RayStation MC with criteria of 3%/3 mm/10%, 3%/2 mm/10%, and 2%/2 mm/10%, respectively.

Patient # γ-pass rate (%) 3%/3 mm γ-pass rate (%) 3%/2 mm γ-pass rate (%) 2%/2 mm time (s)
MC2 VPMC MC2 VPMC MC2 VPMC MC2 VPMC
1 98.01 99.87 97.34 99.83 95.37 98.89 163.54 10.59
2 99.65 99.21 99.44 98.76 97.30 95.90 46.48 4.36
3 99.46 96.41 98.72 94.10 93.91 87.13 78.32 8.42
4 98.61 98.73 98.16 98.36 94.06 94.72 82.07 7.57
5 99.31 99.36 99.13 99.02 97.40 97.10 84.98 3.59
6 95.06 99.61 93.34 99.23 89.61 97.23 93.86 4.44
7 96.84 96.17 95.96 95.22 91.14 91.04 80.07 6.74
8 99.85 99.79 99.75 99.65 98.75 98.59 419.16 25.16
9 96.72 95.90 96.95 94.69 91.77 90.24 18.23 3.25
10 99.60 99.60 99.05 99.07 96.41 96.74 57.82 7.91
Mean 98.31 98.47 97.78 97.79 94.57 94.76 112.45 8.20
SD 1.62 1.63 1.97 2.21 3.02 3.96 114.08 6.42
P-value 0.77 0.70 1.0 —
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abbreviations: MC2 for MCsquare, SD for standard deviation.

2.3. Robust treatment planning

Three typical patients, patient 3 (SRS with a range shifter), patient 5 (SRS without a range shifter), and patient 7 (5 fraction SBRT with a range shifter) were selected for robust optimization using the enhanced VPMC. Our institutional guidelines on the dose volume constraints (DVCs) for PBSPT-based SRS/SBRT in the treatment of brain cancers, based on the version for photon-based SRS/SBRT in the treatment of brain cancer, was used and listed in table 3. Only the DVCs for targets were listed since the DVCs for OARs were easily met for the three selected patients. CIx%⩽y1~y2 is the conformity index (CI) constraint, where CIx% was defined as the ratio of the volume enclosed by the x% iso-dose (x% of the prescription dose) to the volume of the structure of interest (SOI). This CI constraint has a soft upper limit (better below) y1 and a hard limit (must below) y2. Similarly, RHIx%⩽y1~y2 is the radical dose homogeneity index (RHI) with RHIx% defined as the ratio of the maximum dose within the SOI to the x% of the prescription dose.

Table 3.

Target DVH indices of the robustly optimized plans for the three representative patients.

Patient 3 Patient 5 Patient 7
V100% (%, ⩾99%) 99.03 100.00 99.82
Dmin (%, ⩾90%) 97.65 100.13 94.49
CI100% (⩽1.5 ~ 2.0) 1.94 1.73 1.96
RHI100% (⩽1.3 ~ 1.4) 1.15 1.13 1.19
IM calculation time (s) 48.9 27.4 48.5
Optimization time (s) 80.1 40.8 93.3
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abbreviations: CI for conformity index, RHI for radical dose homogeneity index, DVC for dose–volume constraint

For robust optimization, the proton range uncertainty was modelled by scaling the CT’s relative-to-water-stopping-power-ratio by ±3%. The patient setup uncertainty was modelled by shifting the isocenter positively and negatively in all three cardinal directions with a magnitude of 2 mm per out institutional protocol. In total, 13 uncertainty scenarios were included in the robust optimization. Per our institutional protocol, single-field optimization (SFO) was the preferred method for robust optimization. Alternative multiple-field optimization (MFO) would be used if SFO failed to meet the clinical requirements.

To generate the patient-specific aperture opening edge, a 1 mm margin was first added to the CTV to form the planning target volume (PTV). Then PTV which was further expanded with a 2 mm margin to form the patient-specific aperture opening edge to have good target coverage.

3. Results

3.1. Single beamlet validation in water phantom

Three typical proton energies (low, medium, and high) were selected to illustrate the results: 82.0, 140.2, and 228.8 MeV (figure S-1). For both machines (AP and APRS), the percentage depth dose (PDD) curve and the integrated depth dose (IDD) curve from dose distributions calculated by VPMC and MCsquare were compared and found to be in excellent agreement. The 3D gamma passing rates were 99.55% on average with the minimum of 98.78%, under the 2%/2 mm/10% criterion (table S-1).

3.2. Energy layer validation in water phantom

The IDD curves (top row in figure 2), log PDD curves (middle row in figure 2), and iso-dose contours in the transverse plane (20% and 80% of the maximum dose, bottom row in figure 2) were compared between the doses distributions calculated by MCsquare and VPMC for ConfigA (see figure S-2 for ConfigB). In figure 2, from left to right, each column corrsponded to an aperture block opening size, 1, 2, 3, and 4 cm, respectively. Results calculated by VPMC agreed well with the results calculated by MCsquare (curves and contours are largely overlapped). In the 3D gamma analysis, the average passing rate of all validation scenarios (ConfigA and ConfigB) was 99.71 ± 0.23% (table S-2).

Figure 2.

Figure 2.

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Results of the energy layer validation in homogenous water phantoms with ConfigA. Row (a) are the IDD curves, (b) log PDD curves, and (c) contours of iso-dose contours (20% and 80% of the maximum dose) in the transverse planes. From left to right, columns display the results calculated with aperture openings from 1 cm to 4 cm, respectively. Blue lines are the results calculated by MCsquare, while orange lines are the results calculated by VPMC.

3.3. Treatment plan dose validation in patient geometries

Table 2 showed the 3D Gamma passing rates by comparing the dose distributions calculated by MCsquare and VPMC to those calculated by RayStation MC, respectively, which were 98.31 ± 1.62% and 98.47 ± 1.63% with the criterion of 3%/3 mm/10% (the former was MCsquare Versus RayStation MC while the latter was VPMC Versus RayStation MC hereafter), 97.78 ± 1.97% and 97.79 ± 2.21% with the criterion of 3%/2 mm/10%, and 94.57 ± 3.02% and 94.76 ± 3.96% with the criterion of 3%/2 mm/10%. No statistically significant differences of the 3D Gamma passing rates were found between the results calculated by MCsquare and by VPMC (p = 0.77, 0.70, and 1.0, respectively), indicating a comparable simulation accuracy between VPMC and MCsquare. The calculation time was drastically decreased from 112.45 ± 114.08 s when using MCsquare to 8.20 ± 6.42 s when using VPMC.

Two representative patients (patient 5 without range shifter and patient 7 with range shifter) were selected for comparison of the dose distributions calculated by VPMC, MCsquare, and RayStation MC (figure 3(a)–(c) for patient 5 and figure 3(d)–(f) for patient 7). The dose profiles longitudinal (figure 3(b) (e)) and perpendicular (figure 3(c) (f)) to the beam axis in the target region agreed well among VPMC, MCsquare, and RayStation MC.

Figure 3.

Figure 3.

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Dose distributions on a transverse plane of patient 5 ((a)-(c)) and patient 7 ((d)-(f)) calculated by VPMC. Red contours are CTVs. Dose profiles are compared in (b) (e) longitudinal direction (horizontal x arrows in (a) and (d)) and (c) (f) lateral direction (vertical y arrows in (a) and (d)). Results with the aperture block from RayStation MC, VPMC, and MCsquare are in green, blue and purple, respectively.

3.4. Robust optimization

The robustly optimized plans using the enhanced VPMC dose engine for the 3 representative patients all met the DVCs of the targets per our institutional protocol (table 3). In contrast, the robustly optimized plans using the original VPMC (without modelling the aperture block) when adopting the same spot arrangements and DVCs in the robust optimization, did not always meet the DVCs of the targets (table 3). The mean calculation time for 13 influence matrices in robust optimization by VPMC was 41.6 s and the subsequent on-the-fly ‘trial-and-error’ optimization procedure took 71.4 s on average for the selected three patients.

4. Discussion

In this work, we enhanced a fast proton dose engine, VPMC (Shan et al 2022), to support the aperture block to achieve fast MC-based dose calculation (within seconds) and robust optimization (within a couple of minutes) for PBSPT-based SRS to treat brain cancer. The aperture block has been proposed to sharpen the target dose penumbra in PBSPT-based SRS to better protect the nearby normal tissues. The crossing number algorithm (Holmes et al 2022a) was adopted to model the aperture block, which led to more accurate modelling of the aperture block opening for proton dose calculation. Of note, even though the use of SRS with a small CTV margin has largely increased the dose conformity and compactness, the patient setup uncertainties and proton range uncertainties still need to be carefully addressed, which necessitates robust optimization. To model such aperture blocks in robust optimization, the current MC-based dose engines in PBSPT have various issues: either too slow for routine clinical use or inaccurate due to the imperfect modelling of aperture openings. The proposed method can overcome the limitations of the existing MC-based dose engines in PBSPT and achieve seconds-level dose calculation and minutes-level robust optimization with high accuracy in PBSPT-based SRS to treat brain cancer patients.

The margins (CTV to PTV and PTV to the aperture opening edge) used in the design of the aperture was carefully considered during the commissioning to take possible clinical factors into consideration. The 1 mm CTV to PTV margin was chosen based on our institution’s current image-guided radiation therapy (IGRT) protocol for SRS. The additional 2 mm expansion from PTV to the aperture opening was chosen to achieve more homogenous target coverage (Wang et al 2015). We have tried 1 mm and zero mm expansion, which resulted in much less homogenous dose distribution in the target.

In the validations in water phantoms, some mismatches between the IDD curves calculated by VPMC and MCsquare were observed in the entrance region, especially for smaller aperture openings (figure 2[a] and figure S-2[a]). We did not pay much attention to such mismatches because we assumed mismatches of such level of magnitude (the larges mismatch with 1 cm diameter was less than 5% compared to the Bragg peak dose) in the entrance region would have limited impact clinically. Possible reasons for such mismatches could be the different methods to model the opening of apertures and the slit scattered protons among RayStation MC, VPMC and MCsquare. Further research to investigate this small difference will be done in the future.

Overall, the 3D Gamma passing rates for the validations in water phantoms outperformed those in the patient geometries. There are two possible reasons: first, the heterogeneities in patient geometries might introduce uncertainties in the dose calculation; second, the dose calculation resolution used for validation in the water phantoms was half of the one used for validation in the patient geometries (1 mm Versus 2 mm). Given that the target volumes were rather small (mean: 8.32 c.c. and 4.50 c.c. when excluding the largest one with a volume of 43.3 c.c.) in the selected patients, the routinely used dose calculation resolution (2–3 mm) might not be small enough to calculate doses for the selected patients accurately. In order to understand the possible impact of the dose calculation resolution upon the final dose distributions calculated by MCsquare and VPMC, we had conducted the same dose calculations for the selected 10 patients with a dose calculation resolution of 2 mm and 1 mm, respectively. An obvious increase of the 3D Gamma passing rates was observed when changing the dose resolution from 2 mm to 1 mm, especially for the 2%/2 mm criterion where the 3D Gamma passing rate was increased from 96.94 ± 2.82% to 99.05 ± 1.10% (P-value = 0.002) (table S-3). This suggested that in the PBSPT-based SRS treatment for small tumors, the dose calculation resolution should be cautiously selected (the smaller the better) for the treatment plan optimization and dose calculation.

The introduction of apertures could raise the concern of neutron contamination. The neutron dose contribution was neglected in MCsquare and VPMC for its low contribution (<0.5%) (Paganetti 2002, Fippel and Soukup 2004). Similar simplifications were adopted in RayStation GPU MC as well (Fracchiolla et al 2021). Such simplifications were validated by benchmarks against fully blown MC codes (e.g. Geant4) and measurements (Sorriaux et al 2017, Deng et al 2020). A recent study (Holmes et al 2022b) reported a dosimetric assessment of the neutron dose from different aperture materials and found brass was only second to nickel in terms of neutron generation. Given the other advantages, e.g. efficient stopping power and easy to fabricate, brass apertures are commonly used in passive scattering proton therapy (PSPT) and PBSPT. Another study investigated the impact of employing a patient-specific aperture in PBSPT and found the neutron dose equivalent for out-of-field organs showed no significant difference between PBSPT with and without apertures (Geng et al 2016). In fact, the neutron contamination was less for PBSPT because only the aperture was used to reduce the spot sizes, instead of shaping a broad beam in PSPT or collimating every spot in the scanning spot aperture (Holmes et al 2022b). Besides, the benefit of largely reduced lateral penumbra of target dose offered by the aperture could outweigh the concern for secondary cancers caused by neutrons stemming from the aperture (Geng et al 2016). Nonetheless, we do think neutron contamination (and contaminations from other nuclear products) needs a quantitative investigation for such a new technology before clinical adoption and a subsequent study is warranted.

This study has certain shortcomings. First, the aperture block used in this study is that it is non-divergent, which could lead to collimator contamination problem by the edge-scattered protons, especially for shallow tumors with adjacent lateral and proximal OARs. A divergent aperture block could help mitigate this problem (Zhao et al 2015, Hyer et al 2021), which will be our next step to further enhance the benefits of the use of the aperture block in the PBSPT-based SRS treatment for brain cancer patients with shallow small targets. Second, patient-specific aperture used in this study was fabricated according to the largest tumor cross-section (plus some margin) from the beam eye view, thus only improving the dose lateral penumbra at the depth with the largest tumor cross-section. In the future, we will investigate the feasibility of an energy-layer-specific dynamic aperture to cover the whole target in all depths, i.e. the whole target in the beam direction.

5. Conclusion

In this work, we have enhanced VPMC to model aperture blocks used in the PBSPT-based SRS in the treatment of brain cancer patients with small targets. The enhancement includes both fast MC-based dose calculation (average 8.2 s) and fast robust optimization (average 113.0 s). The benchmark results against MCsquare in water phantoms and against MCsquare/RayStation MC in patient geometries are excellent. Our enhanced VPMC can be used to robustly optimize a PBSPT-based SRS plan efficiently and accurately.

Supplementary Material

Supplemental Materials

Funding statement

This research was supported by the National Cancer Institute (NCI) Career Developmental Award K25CA168984, Arizona Biomedical Research Commission Investigator Award, the Lawrence W and Marilyn W Matteson Fund for Cancer Research, and the Kemper Marley Foundation.

Footnotes

Conflict of Interest: None

Ethical statement

This research was approved by the Mayo Clinic Arizona institutional review board (IRB, 13-005709). The informed consent was waived by IRB protocol. Only image and dose–volume data were used in this study. All patient-related health information was removed prior to the analysis and also publication of the study. This research was conducted in accordance with the principles embodied in the Declaration of Helsinki and in accordance with local statutory requirements.

Supplementary material for this article is available online

Data availability statement

All data that support the findings of this study are included within the article (and any supplementary information files). Research data are stored in an institutional repository and will be shared upon request to the corresponding author.

References

  1. Amelio D et al. 2019. P14.75 Active beam scanning proton therapy radiosurgery: early outcomes Neuro-Oncology 21 iii85–ii85 [Google Scholar]
  2. Atkins KM et al. 2018. Proton stereotactic radiosurgery for brain metastases: a single-institution analysis of 370 patients Int. J. Radiat. Oncol. Biol. Phys 101 820–9 [DOI] [PubMed] [Google Scholar]
  3. Bäumer C, Fuentes C, Janson M, Matic A, Timmermann B and Wulff J 2019. Stereotactical fields applied in proton spot scanning mode with range shifter and collimating aperture Phys. Med. Biol 64 155003. [DOI] [PubMed] [Google Scholar]
  4. Benedict SH et al. 2010. Stereotactic body radiation therapy: The report of AAPM Task Group 101 Med. Phys 37 4078–101 [DOI] [PubMed] [Google Scholar]
  5. Bussiere M. et al. Proton radiosurgery: a clinical transition from passive scattering to pencil beam scanning. Int. J. Radiat. Oncol.*Biol.*Phys. 2021;111:e544. [Google Scholar]
  6. Deng W et al. 2020. Technical note: integrating an open source Monte Carlo code ‘MCsquare’ for clinical use in intensity-modulated proton therapy Med. Phys 47 2558–7s4 [DOI] [PubMed] [Google Scholar]
  7. Dowdell SJ. et al. Monte Carlo study of the potential reduction in out-of-field dose using a patient-specific aperture in pencil beam scanning proton therapy. Phys. Med. Biol. 2012;57:2829. doi: 10.1088/0031-9155/57/10/2829. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Fellin F et al. 2019. Is it beneficial to use apertures in proton radiosurgery WITH a scanning beam? a dosimetric COMPARISON Int. J. Radiat. Oncol. Biol. Phys 105 E760–1 [DOI] [PMC free article] [PubMed] [Google Scholar]
  9. Feng H et al. 2022a. Per-voxel constraints to minimize hot spots in linear energy transfer (LET)-guided robust optimization for base of skull head and neck cancer patients in IMPT Med. Phys 49 632–47 [DOI] [PubMed] [Google Scholar]
  10. Feng H et al. 2021. Technical note: 4D robust optimization in small spot intensity-modulated proton therapy (impt) for distal esophageal carcinoma Med. Phys 48 4636–47 [DOI] [PubMed] [Google Scholar]
  11. Feng H et al. 2022b. GPU-accelerated Monte Carlo-based online adaptive proton therapy: a feasibility study Med. Phys 49 3550–63 [DOI] [PubMed] [Google Scholar]
  12. Fippel M and Soukup M 2004. A Monte Carlo dose calculation algorithm for proton therapy Med. Phys 31 2263–73 [DOI] [PubMed] [Google Scholar]
  13. Fracchiolla F et al. 2021. Clinical validation of a GPU-based Monte Carlo dose engine of a commercial treatment planning system for pencil beam scanning proton therapy Phys. Med 88 226–34 [DOI] [PubMed] [Google Scholar]
  14. Frank SJ et al. 2014. Multifield optimization intensity modulated proton therapy for head and neck tumors: a translation to practice Int. J. Radiat. Oncol. Biol. Phys 89 846–53 [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Fredriksson A, Forsgren A and Hardemark B 2011. Minimax optimization for handling range and setup uncertainties in proton therapy Med. Phys 38 1672–84 [DOI] [PubMed] [Google Scholar]
  16. Geng C, Moteabbed M, Xie Y, Schuemann J, Yock T and Paganetti H 2016. Assessing the radiation-induced second cancer risk in proton therapy for pediatric brain tumors: the impact of employing a patient-specific aperture in pencil beam scanning Phys. Med. Biol 61 12. [DOI] [PubMed] [Google Scholar]
  17. Halasz LM et al. 2011. Proton stereotactic radiosurgery for the treatment of benign meningiomas Int. J. Radiat. Oncol.*Biol.*Phys 81 1428–35 [DOI] [PubMed] [Google Scholar]
  18. Holmes J et al. 2022a. Technical note: evaluation and second check of a commercial Monte Carlo dose engine for small-field apertures in pencil beam scanning proton therapy Med. Phys 49 3497–506 [DOI] [PubMed] [Google Scholar]
  19. Holmes J et al. 2022b. Collimating individual beamlets in pencil beam scanning proton therapy, a dosimetric investigation Front Oncol. 12 1031340. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Huang S et al. 2018. Validation and application of a fast Monte Carlo algorithm for assessing the clinical impact of approximations in analytical dose calculations for pencil beam scanning proton therapy Med. Phys 45 5631–42 [DOI] [PubMed] [Google Scholar]
  21. Hyer DE, Bennett LC, Geoghegan TJ, Bues M and Smith BR 2021. Innovations and the use of collimators in the delivery of pencil beam scanning proton therapy Int. J. Part. Ther 8 73–83 [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Liu C et al. 2020. Robust optimization for intensity-modulated proton therapy to redistribute high linear energy transfer (LET) from nearby critical organs to tumors in head and neck cancer Int. J. Radiat. Oncol. Biol. Phys 107 181–93 [DOI] [PubMed] [Google Scholar]
  23. Liu C. et al. Fast MCsquare-based independent dose verification platform for pencil beam scanning proton therapy. Technol. Cancer Res. Treat. 2021;20 doi: 10.1177/15330338211033076. 15330338211033076. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Liu W et al. 2016. Exploratory Study of 4D versus 3D robust optimization in intensity modulated proton therapy for lung cancer Int. J. Radiat. Oncol. Biol. Phys 95 523–33 [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Liu W, Li Y, Li X, Cao W and Zhang X 2012b. Influence of robust optimization in intensity-modulated proton therapy with different dose delivery techniques Med. Phys 39 3089–101 [DOI] [PMC free article] [PubMed] [Google Scholar]
  26. Liu W, Zhang X, Li Y and Mohan R 2012a. Robust optimization of intensity-modulated proton therapy Med. Phys 39 1079–91 [DOI] [PMC free article] [PubMed] [Google Scholar]
  27. Low DA, Harms WB, Mutic S and Purdy JA 1998. A technique for the quantitative evaluation of dose distributions Med. Phys 25 656–61 [DOI] [PubMed] [Google Scholar]
  28. Maes D. et al. Parametric characterization of penumbra reduction for aperture-collimated pencil beam scanning (PBS) proton therapy. Biomed. Phys. Eng. Express. 2019;5:035002. [Google Scholar]
  29. Milano MT et al. 2021. Single-and multifraction stereotactic radiosurgery dose/volume tolerances of the brain Int. J. Radiat. Oncol.* Biol.* Phys 110 68–86 [DOI] [PMC free article] [PubMed] [Google Scholar]
  30. Moteabbed M, Yock TI, Depauw N, Madden TM, Kooy HM and Paganetti H 2016. Impact of spot size and beam-shaping devices on the treatment plan quality for pencil beam scanning proton therapy Int. J. Radiat. Oncol.*Biol.*Phys 95 190–8 [DOI] [PMC free article] [PubMed] [Google Scholar]
  31. Paganetti H. Nuclear interactions in proton therapy: dose and relative biological effect distributions originating from primary and secondary particles. Phys. Med. Biol. 2002;47:747. doi: 10.1088/0031-9155/47/5/305. [DOI] [PubMed] [Google Scholar]
  32. Pflugfelder D, Wilkens JJ and Oelfke U 2008. Worst case optimization: a method to account for uncertainties in the optimization of intensity modulated proton therapy Phys. Med. Biol 53 1689–700 [DOI] [PubMed] [Google Scholar]
  33. Rana S et al. 2021. Investigating the utilization of beam-specific apertures for the intensity-modulated proton therapy (IMPT) head and neck cancer plans Med. Dosim 46 e7–11 [DOI] [PubMed] [Google Scholar]
  34. Schild SE et al. 2014. Proton beam therapy for locally advanced lung cancer: a review World J. Clin. Oncol 5 568–75 [DOI] [PMC free article] [PubMed] [Google Scholar]
  35. Shan J et al. 2020. Intensity-modulated proton therapy (IMPT) interplay effect evaluation of asymmetric breathing with simultaneous uncertainty considerations in patients with non-small cell lung cancer Med. Phys 47 5428–40 [DOI] [PMC free article] [PubMed] [Google Scholar]
  36. Shan J et al. 2022. Virtual particle Monte Carlo: a new concept to avoid simulating secondary particles in proton therapy dose calculation Med. Phys 49 6666–83 [DOI] [PMC free article] [PubMed] [Google Scholar]
  37. Shan J, Sio TT, Liu C, Schild SE, Bues M and Liu W 2018. A novel and individualized robust optimization method using normalized dose interval volume constraints (NDIVC) for intensity-modulated proton radiotherapy Med. Phys 46 382–93 [DOI] [PubMed] [Google Scholar]
  38. Shen J et al. 2023. Technical note: comprehensive evaluations of gantry and couch rotation isocentricities for implementing proton stereotactic radiosurgery Med. Phys 50 3359–67 [DOI] [PubMed] [Google Scholar]
  39. Shen J et al. 2015. Impact of range shifter material on proton pencil beam spot characteristics Med. Phys 42 1335–53 [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. Shen J et al. 2016. An efficient method to determine double Gaussian fluence parameters in the eclipse proton pencil beam model Med. Phys 43 6544–51 [DOI] [PMC free article] [PubMed] [Google Scholar]
  41. Shen J. et al. Using field size factors to characterize the in-air fluence of a proton machine with a range shifter. Radiat. Oncol. 2017a;12:52. doi: 10.1186/s13014-017-0783-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  42. Shen J et al. 2017b. Technical note: using experimentally determined proton spot scanning timing parameters to accurately model beam delivery time Med. Phys 44 5081–8 [DOI] [PubMed] [Google Scholar]
  43. Shimrat M. Algorithm 112: position of point relative to polygon. Commun. ACM. 1962;5:434. [Google Scholar]
  44. Sorriaux J et al. 2017. Experimental assessment of proton dose calculation accuracy in inhomogeneous media Phys. Med 38 10–5 [DOI] [PubMed] [Google Scholar]
  45. Souris K, Lee JA and Sterpin E 2016. Fast multipurpose Monte Carlo simulation for proton therapy using multi- and many-core CPU architectures Med. Phys 43 1700–12 [DOI] [PubMed] [Google Scholar]
  46. Titt U, Zheng Y, Vassiliev ON and Newhauser WD 2008. Monte Carlo investigation of collimator scatter of proton-therapy beams produced using the passive scattering method Phys. Med. Biol 53 487–504 [DOI] [PubMed] [Google Scholar]
  47. Unkelbach J. et al. Robust radiotherapy planning. Phys. Med. Biol. 2018;63:22TR02. doi: 10.1088/1361-6560/aae659. [DOI] [PubMed] [Google Scholar]
  48. Unkelbach J, Bortfeld T, Martin BC and Soukup M 2009. Reducing the sensitivity of IMPT treatment plans to setup errors and range uncertainties via probabilistic treatment planning Med. Phys 36 149–63 [DOI] [PMC free article] [PubMed] [Google Scholar]
  49. Wagenaar D. et al. Validation of linear energy transfer computed in a Monte Carlo dose engine of a commercial treatment planning system. Phys. Med. Biol. 2020;65:025006. doi: 10.1088/1361-6560/ab5e97. [DOI] [PubMed] [Google Scholar]
  50. Wang D. et al. Impact of spot size on plan quality of spot scanning proton radiosurgery for peripheral brain lesions. Med. Phys. 2014;41:121705. doi: 10.1118/1.4901260. [DOI] [PubMed] [Google Scholar]
  51. Wang D, Smith BR, Gelover E, Flynn RT and Hyer DE 2015. A method to select aperture margin in collimated spot scanning proton therapy Phys. Med. Biol 60 N109–N119 [DOI] [PubMed] [Google Scholar]
  52. van de Water TA, Lomax AJ, Bijl HP, Schilstra C, Hug EB and Langendijk JA 2012. Using a reduced spot size for intensity-modulated proton therapy potentially improves salivary gland-sparing in oropharyngeal cancer Int. J. Radiat. Oncol.*Biol.*Phys 82 e313–9 [DOI] [PubMed] [Google Scholar]
  53. Widesott L, Lorentini S, Fracchiolla F, Farace P and Schwarz M 2018. Improvements in pencil beam scanning proton therapy dose calculation accuracy in brain tumor cases with a commercial Monte Carlo algorithm Phys. Med. Biol 63 145016. [DOI] [PubMed] [Google Scholar]
  54. Yamamoto M et al. 2014. Stereotactic radiosurgery for patients with multiple brain metastases (JLGK0901): a multi-institutional prospective observational study Lancet Oncol. 15 387–95 [DOI] [PubMed] [Google Scholar]
  55. Yang Y et al. 2021. Exploratory investigation of dose-linear energy transfer (LET) volume histogram (DLVH) for adverse events study in intensity modulated proton therapy (IMPT) Int. J. Radiat. Oncol. Biol. Phys 110 1189–99 [DOI] [PubMed] [Google Scholar]
  56. Yang Y et al. 2022. Exploratory study of seed spots analysis to characterize dose and linear-energy-transfer effect in adverse event initialization of pencil-beam-scanning proton therapy Med. Phys 49 6237–52 [DOI] [PubMed] [Google Scholar]
  57. Yasui K et al. 2015. A patient-specific aperture system with an energy absorber for spot scanning proton beams: verification for clinical application Med. Phys 42 6999–7010 [DOI] [PubMed] [Google Scholar]
  58. Zhao T, Cai B, Sun B, Grantham K, Mutic S and Klein E 2015. Use of diverging apertures to minimize the edge scatter in passive scattering proton therapy J. Appl. Clin. Med. Phys 16 367–72 [DOI] [PMC free article] [PubMed] [Google Scholar]

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Supplementary Materials

Supplemental Materials
NIHMS1983234-supplement-Supplemental_Materials.docx (537.8KB, docx)

Data Availability Statement

All data that support the findings of this study are included within the article (and any supplementary information files). Research data are stored in an institutional repository and will be shared upon request to the corresponding author.

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