Development and validation of the Dynamic Collimation Monte Carlo simulation package for pencil beam scanning proton therapy

Abstract

Purpose:

The aim of this work was to develop and experimentally validate a Dynamic Collimation Monte Carlo (DCMC) simulation package specifically designed for the simulation of collimators in pencil beam scanning proton therapy (PBS-PT). The DCMC package was developed using the TOPAS Monte Carlo platform and consists of a generalized PBS source model and collimator component extensions.

Methods:

A divergent point-source model of the IBA dedicated nozzle (DN) at the Miami Cancer Institute (MCI) was created and validated against on-axis commissioning measurements taken at MCI. The beamline optics were mathematically incorporated into the source to model beamlet deflections in the X and Y directions at the respective magnet planes. Off-axis measurements taken at multiple planes in air were used to validate both the off-axis spot size and divergence of the source model. The DCS trimmers were modeled and incorporated as TOPAS geometry extensions that linearly translate and rotate about the bending magnets. To validate the collimator model, a series of integral depth dose (IDD) and lateral profile measurements were acquired at MCI and used to benchmark the DCMC performance for modeling both pristine and range shifted beamlets. The water equivalent thickness (WET) of the range shifter was determined by quantifying the shift in the depth of the 80% dose point distal to the Bragg peak between the range shifted and pristine uncollimated beams.

Results:

A source model of the IBA DN system was successfully commissioned against on- and off-axis IDD and lateral profile measurements performed at MCI. The divergence of the source model was matched through an optimization of the source-to-axis distance and comparison against in-air spot profiles. The DCS model was then benchmarked against collimated IDD and in-air and in-phantom lateral profile measurements. Gamma analysis was used to evaluate the agreement between measured and simulated lateral profiles and IDDs with 1%/1 mm criteria and a 1% dose threshold. For the pristine collimated beams, the average 1%/1 mm gamma pass rates across all collimator configurations investigated were 99.8% for IDDs and 97.6% and 95.2% for in-air and in-phantom lateral profiles. All range shifted collimated IDDs passed at 100% while in-air and in-phantom lateral profiles had average pass rates of 99.1% and 99.8%, respectively. The measured and simulated WET of the polyethylene range shifter was determined to be 40.9 and 41.0 mm, respectively.

Conclusions:

We have developed a TOPAS-based Monte Carlo package for modeling collimators in PBS-PT. This package was then commissioned to model the IBA DN system and DCS located at MCI using both uncollimated and collimated measurements. Validation results demonstrate that the DCMC package can be used to accurately model other aspects of a DCS implementation via simulation.

1. INTRODUCTION

Pencil beam scanning proton therapy (PBS-PT) is a radiotherapy treatment delivery technique in which pencil beams of protons are magnetically scanned across a target volume to deliver an intended dose distribution in successive energy layers.¹ This overcomes the limitations of broad beam delivery methods like passive scattering and uniform scanning, where the use of patient-specific apertures only provides collimation for the energy layer with the largest lateral extents in the beam’s eye view (BEV), significantly reducing the achievable conformity in adjacent energy layers.² In uncollimated PBS, the overall target conformity is largely dependent on beam spot size. This is often represented by the standard deviation of the measured Gaussian distribution of the proton beam’s fluence in air at isocenter (σ_air) and broadens with depth due to multiple Coulomb scattering in the patient. Range shifters are used to further degrade the beam for the treatment of shallow targets proximal to the range of the lowest available energy of the beam generation system, contributing to additional spot size broadening.

It has been shown that for brain and head and neck sites, a smaller σ_air leads to a more conformal dose distribution and reduces the normal tissue complication probabilities (NTCP) resulting from proton therapy.^3–8 Although achievable spot sizes are shrinking due to improved beam focusing systems, the lateral dose fall-off remains one of the limiting factors impacting dose conformity.⁹ A dynamic collimation system (DCS) is under development to improve lateral conformity in PBS-PT. The DCS consists of two pairs of orthogonal nickel collimating trimmers that move in synchrony with the proton pencil beam to intercept and effectively “trim” the pencil beam at the edge of the target.^10,11 The DCS is designed to be mounted to a proton nozzle, minimizing the air gap between the collimators and the patient. As the DCS approaches clinical implementation, a large effort has been placed on integrating the DCS with an existing, FDA-approved treatment planning system to enable planning and optimization of DCS-collimated treatments.

While a full Monte Carlo simulation can most accurately model the DCS, pencil beam algorithms enable fast treatment planning and optimization. These algorithms are especially important considering the computational intensity required for treatment planning with the DCS, where both spot and trimmer placements need to be simultaneously optimized.¹² This requires that substantially more beamlets are calculated during the DCS-based treatment planning process than for standard pencil beam scanning, and many of the beamlet calculations are done on-the-fly during the optimization process as the DCS positions converge. While many authors have published GPU-based Monte Carlo planning tools,^13–15 there are currently no FDA-approved Monte Carlo-based treatment planning systems that support the use of divergent collimators such as the DCS trimmers. Because of this, we expect that the additional complexity associated with trimmer optimization would be best suited for analytical methods that have been benchmarked using a general purpose Monte Carlo code that can fully model the divergence of the DCS trimmers. The pencil beam algorithm for proton dose calculations proposed by Hong et al. approximates beam-shaping devices (collimators, apertures, blocks) as infinitesimally thin fluence blocking apertures and ignores any out-scatter from these devices when calculating patient dose distributions.¹⁶ Although Hong’s algorithm is fast and generally suitable for treatment planning, it exhibits noticeable discrepancies in both heterogeneous media and regions downstream of beam-shaping devices that led to the development of more sophisticated analytical calculation methods.^17–21 These algorithms were developed on the basis of extensive Monte Carlo simulations that provide vital information as to what effects should be incorporated into quick, accurate, and robust algorithms.

Considering the DCS is still under development, a Dynamic Collimation Monte Carlo (DCMC) package has been developed to provide useful insights into the appropriateness of analytical dose calculation algorithms and future experimental measurements with the DCS. Consisting of a generic pencil beam scanning source model and collimator geometry components, the DCMC package will be available publicly for download to aid other researchers in modeling collimators for PBS applications. The following work describes the development and validation of the DCMC simulation package specific to the DCS and Ion Beam Applications (IBA, Belgium) Dedicated Nozzle (DN) delivery system at the Miami Cancer Institute (MCI).

2. MATERIALS AND METHODS

2.A. Beam model

The source model in the DCMC package consists of a divergent point source placed at some user-specified source-to-axis distance (SAD) above the bending magnets. Instead of simulating the magnetic fields, beamlet deflections were mathematically incorporated into the source through the use of a particle generator extension to the Geant4-based application TOPAS.^22,23 The general workflow of the source extension is illustrated in Fig. 1, where trajectories are sampled at the point source and projected to the X magnet plane. A source model was commissioned to represent the IBA DN delivery system located at the MCI using on- and off-axis commissioning measurements to model the energy spectra, divergence, spot size, and off-axis behavior of the source. An emphasis was placed on accurately modeling beam divergence as it is expected that a majority of beamlets collimated by the DCS will be significantly deflected off-axis near the periphery of a target. It should be noted that the steps outlined in this work were taken to ensure accurate modeling the MCI IBA DN system specifically, and that any users of the DCMC package must undergo a similar process for accurately commissioning a source model specific to the beamline which they are investigating.

Fig. 1.

Schematic of source sampling technique and deflections used in the TOPAS beam model.

2.A.1. On-axis validation

The on-axis commissioning measurements consisted of integrated depth dose (IDD) curves, in-air spot profiles (σ_air), and IAEA TRS-398 absolute dose measurements (cGy/MU) for nominal energies ranging from 70 to 160 MeV in 5 MeV intervals. This energy range was selected as it has been previously shown that collimation provides the most benefits at lower beam energies.⁹ IDD curves were measured in water using a large-area (12 cm active diameter) Stingray parallel plate ionization chamber²⁴ (IBA Dosimetry, Germany) with a 0.1-mm scanning resolution in depth around the Bragg peak. In-air spot profiles were acquired at isocenter and at planes 100 and 200 mm upstream and downstream from isocenter using the two-dimensional Lynx scintillation detector^25,26 (IBA Dosimetry, Germany) to capture both the spot size and divergence of the beam. Absolute dose measurements were performed with a 10-mm diameter parallel plate ionization chamber (PPC05, IBA Dosimetry, Germany) placed in monoenergetic 10 × 10 cm² square field (2.5 mm spot spacing) at a depth dependent on the beam quality specified in the IAEA TRS-398 absorbed dose to water protocol for proton beams.²⁷

A divergent point source model of the IBA DN beamline was developed by directly sampling from the measured asymmetric lateral intensity distributions and adjusting TOPAS source parameters to match IDD curves and off-axis measurements. A back projection method was used to derive the angular distribution of the point source by sampling the lateral profile measurements at isocenter and back-projecting these samples to a user-specified SAD. Because this sampling approach will inherently reproduce the measurements at isocenter, the SAD was optimized using iterative methods to optimize agreement at all other measurement planes in-air thereby creating a divergence-matched source. This was done for 85, 110, 130, and 160 MeV beams for spot sizes in X and Y at all measurement planes prior to modeling the beam’s deflection.

The IBA DN system at MCI has X and Y bending magnets located at 182.5 and 219.5 cm above isocenter, respectively. Therefore, the divergent point source commissioned on-axis was extended to include magnet-specific deflections downstream from the initial sampled trajectory (r_samp) given a user-specified spot location (X_pos, Y_pos) and SAD as illustrated in Fig. 1. The emission vector where particles are first generated in the Monte Carlo simulation can be described by the position vector.

$${\overrightarrow{r}}_{emit}={\overrightarrow{P}}_X+R_Y{R}_X{\widehat{r}}_{samp}$$ (1)

where ${\overrightarrow{P}}_X$ is the spatial location of the sampled trajectory at the X magnet plane, R_Y and R_X correspond to rotation matrices that account for the user-specified spot location in X and Y, and ${\widehat{r}}_{samp}$ is an initial sampled trajectory at the commissioned SAD. For every primary proton generated, the TOPAS source extension computes the quantities in Eq. (1) and begins tracking downstream from the X magnet plane.

Energy spectra for all commissioned energies were assumed to be Gaussian and were estimated using an optimization method technique similar to that described by Ardenfors.²⁸ IDD curves were simulated and scored using a 12-cm cylindrical mesh tally with a depth resolution of 0.1 mm. The mean energy and variance of the energy spectra were iteratively adjusted to match the measured IDDs using the depth and the full width at half maximum (FWHM) of the Bragg peak, the depth of the distal 80% dose (R80), and overall gamma pass rates as agreement metrics. The model’s output was determined by relating the absorbed dose-to-water measurement to simulation results under identical reference conditions specified by TRS-398 and calculating the number of protons per MU using Eq. (2):

$${\left(\frac{N_{protons}}{MU}\right)}_{MC}=\frac{D_{meas}}{D_{MC}}$$ (2)

where D_meas is the measured dose in cGy per MU and D_MC is the simulated dose in cGy per number of protons.

2.A.2. Off-axis validation

This step in the modeling process was taken to verify that the magnet-specific deflections implemented are representative of measured off-axis data. To do this, two-dimensional Lynx spot maps of beamlets deflected 5 cm in X, Y, X & Y, and one on-axis beamlet (nine total beamlets) were measured at isocenter as well as 10 cm upstream and downstream along the beam axis to verify both the off-axis spot size and divergence for the 85, 110, and 160 MeV beams. The two-dimensional Lynx measurements were compared to identical simulations to ensure the off-axis spot size and divergence of the source model were representative of the measured data. To account for any uncertainties in the setup of the Lynx, a 2D rigid optimization consisting of rotations and translations was used to align the measured profiles with the simulated two-dimensional profiles. For measured points receiving greater than or equal to 1% of the maximum measured dose, overall gamma pass rates with 1%/1 mm criteria and median dose differences were used to quantify the off-axis agreement following the 2D affine optimization.

2.B. DCS Monte Carlo modeling

The beam-modifying DCS components consist of two pairs of nickel trimmer blades located on separate planes (upper and lower) that are mounted downstream from a 4-cm thick polyethylene range shifter. The nickel trimmers are 3 cm thick and 2 cm wide and made of Ni-200 alloy (ρ = 8.908 g/cc) due to its relatively low neutron production and resulting integral dose.²⁹ Polyethylene (ρ = 0.97 g/cc) was selected for the range shifter due to its preservation of spot size and thus, dose conformity.^30,31 The DCS will be mounted to a telescoping accessory tray that can extend and retract resulting in air gaps between the collimator and isocenter that range from 5 cm (fully extended) to 18.15 cm (fully retracted), respectively. The fully extended geometry shown in Fig. 2 was used in this work as this is the more clinically desirable setup to reduce in-air scatter and further broadening of σ_air.

Fig. 2.

Diagram illustrating the overall simulation and DCS parameters for the TOPAS simulations of DCScollimated fields. The source-to-axis distance is determined through optimization done during beam modeling.

The DCS trimmers were incorporated into the beam model through the development of custom Geant4 geometry components that mimic the dynamic motion of the DCS described by Geoghegan et al., where linearly translating trimmer blades simultaneously rotate as they travel away from isocenter to match beam divergence.¹¹ The individual trimmer components of the DCS (X1, X2, Y1, Y2) were added as extensions to the TOPAS application to enable robust 4D simulations of dynamically collimated treatment fields. The inputs to the trimmer components are the spot location (X_spot, Y_spot), the SAD, the X- and Y-trimmer to axis distances (TAD_x and TAD_y), the X- and Y-magnet to axis distances (MAD_x and MAD_y), and a Boolean operator on whether the user would like to collimate the beamlet or not. An optional trimmer offset has also been implemented based on the work of Smith et al., which showed that offsetting the trimmers from the beamlet’s central axis (CAX) adds robustness to the expected delivery in practice.³² If DCS collimation is requested in the TOPAS input file, the trimmer components translate and rotate such that the medial edge of the trimmer coincides with the beamlet’s CAX, in the case where there is no trimmer offset. The medial edge of the X trimmer (X_medial) can be related to the spot location through the geometric relation:

$$X_{medial}=\frac{X_{spot}\cdot \left(MA{D}_x-TA{D}_x\right)}{MA{D}_x}=X_{spot}\cdot \left(1-\frac{TA{D}_x}{MA{D}_x}\right)$$ (3)

However, since TOPAS/Geant4 requires the centroid location of the physical volume for placement, the centroid of the trimmer can be related to the medial edge through:

$$X_{centroid}=X_{medial}\pm \frac{0.5\cdot W_{trimmer}}{\cos \left({\theta }_{Xspot}\right)}\pm {\Delta }_{offset}$$ (4)

where W_trimmer is the 2 cm width of the trimmers and θ_Xspot is the beamlet deflection angle between the beamlet’s central axis and the desired spot position $X_{spot}({\theta }_{Xspot}={\tan }^{-1}(\frac{X_{spot}}{MA{D}_x}))$. The polarity of the plus/minus operators depends on which specific trimmer (e.g., X1 vs X2) is being positioned. A rendering of the TOPAS DCS model is displayed in Fig. 3.

Fig. 3.

Rendering of the DCS TOPAS model with primary protons (blue) and secondary tracks of electrons (red) and photons (green). The bending magnets were modeled through a TOPAS particle generator extension that applies rotation matrices at the planes of bending magnets and emits particles at the plane of the downstream magnet. The DCS trimmers (dark gray) linearly translate while rotating in their respective trimmer planes. The range shifter and water phantom are also shown in pink and blue, respectively. The bending magnet locations and size are not to scale.

2.C. DCS model validation

Although the model was benchmarked against commissioning and QA measurements performed at MCI, the DCMC package has yet to be experimentally validated against collimated beamlets. Therefore, a set of collimated beamlet measurements consisting of IDD curves and in-air and in-phantom lateral profiles were acquired at MCI to assess the accuracy of the DCMC package. The goals of these measurements were to (a) characterize the influence of the trimmers on the IDD, (b) benchmark the model’s ability to predict relative changes in penumbra resulting from collimation of varying degrees, and (c) to measure and verify the water equivalent thickness (WET) of the polyethylene range shifter and validate its influence on spot size.

IDD curves were acquired with an IBA Giraffe (12 cm diameter collecting electrode) multilayer ionization chamber (MLIC)²⁴ (IBA Dosimetry, Germany) and lateral profiles were measured with the Lynx scintillator. The IBA Giraffe MLIC was selected due to its ability to acquire a large set of IDD curves quickly and efficiently. Although the materials that comprise the Giraffe are water equivalent in length, previous work by Baumer et al showed that the material that lines the inside of the electrode plates exhibits a much lower mass stopping power when compared to water for protons below 50 MeV.²⁴ The rise of the mass stopping-power ratio with decreasing energy below 50 MeV leads to a sharper, more intense Bragg peak in-water than in Giraffe-equivalent material. Therefore, IDD curves acquired with the Giraffe MLIC were corrected to represent an in-water measurement using an energy- and depth-dependent correction function derived from uncollimated Giraffe MLIC measurements and in-water commissioning measurements taken with the Stingray ionization chamber presented in Section 2.A.1.

Measurements were acquired for both pristine and range shifted 90, 125, and 165 MeV beams. Due to the thickness of the trimmer blades, 165 MeV pristine data were only used for measuring the WET of the polyethylene range shifter and were excluded from trimmer characterization measurements. The WET of the range shifter was measured using the range pull-back technique, where the WET is defined as the change in the R80 between a pristine and range shifted beam.³³ For each energy, a set of X, Y, and X & Y (“double trimmed”) trimmer offset combinations were selected to represent both “tightly” and “loosely” collimated beamlets. The “loosely” collimated offsets slightly decrease with increasing energy to account for the larger spot size at lower energies. In-air profiles were acquired by aligning the Lynx to isocenter while in-phantom measurements were acquired by maintaining a constant snout to surface distance (SSD) and placing a predetermined amount of Gammex Solid Water® (Middleton, Wisconsin) proximal to the front face of the Lynx. To reduce the influence of setup uncertainties associated with high-dose gradients such as the Bragg peak, the depth of measurement was intentionally selected to be in the plateau region for both range shifted and pristine beams. A 3 × 3 spot map delivery of beamlets deflected 5 cm off-axis was used for lateral profile measurements, but only the central spot was analyzed for this work. A summary of the energies, trimmer configurations, and measurement depths in Solid Water® (WET = 1.03) is displayed in Table I. The DCS trimmers exhibit symmetry; therefore, measurements were only taken for beamlets collimated by the X2 and Y2 trimmers instead of combinations involving all four trimmers.

Table I.

Summary of trimmer configurations and energies (both pristine and range shifted) investigated. The measurement depth corresponds to the amount of Solid Water® placed proximal to the front face of the Lynx detector.

Beam Energy (MeV)	X2 offset (mm)	Y2 offset (mm)	Measurement depth (mm)
90	1	N/A	10
	5	N/A	10
	N/A	1	10
	N/A	5	10
125	1	N/A	40
	4	N/A	40
	1	4	40
	1	1	40
	4	1	40
	N/A	1	40
	N/A	4	40
165*	1	N/A	80
	3	N/A	80
	N/A	1	80
	N/A	3	80

N/A indicates that the trimmer was placed out of field.

^*Trimmer validation was only performed for range shifted beam.

The DCMC was used to simulate IDD curves in a 0.1-mm cylindrical mesh tally with a 12-cm diameter identical to the active volume of the Giraffe MLIC. Lateral profiles were scored in 0.5 mm³ voxels centered in a 4 mm thick slab of water to mimic the WET to the plane of detection measured by the Lynx scintillation plate. In-phantom lateral profiles were simulated to account for the WET of Solid Water®. Each simulated lateral profile was smoothed with a 2D Gaussian function in MATLAB and measured data underwent a 2D rigid registration consisting of rotations and translations to account for any setup uncertainties with the Lynx.

3. RESULTS

3.A. On-axis beam model

Figure 4 qualitatively illustrates the model’s performance for IDD curves, lateral profiles at isocenter, and comparison with a 2D Lynx measurement at isocenter. The R80, Depth of the Bragg peak, FWHM, and overall gamma pass rate agreement metrics used for the IDD commissioning are displayed in Fig. 5. For nominal energies ranging from 70 to 160 MeV, the average 1D gamma pass rates were 99.39% and 91.22% with 1%/1 and 0.5%/0.5 mm evaluation criteria, respectively. The measured and simulated R80 and depth of the Bragg peak were verified to within 0.2% and the FWHM of the Bragg peak was within 1 mm on average.

Fig. 4.

(a) Integral depth dose curves (IDDs) of Monte Carlo results overlaid with commissioning measurements. (b) Simulated and measured 100 MeV lateral intensity X profiles at isocenter. (c) Simulated and measured 100 MeV lateral intensity Y profiles at isocenter. (d) 85 MeV 2D in-air profile overlaid with measured 2D Lynx profile of beamlet.

Fig. 5.

(a) Depth of Bragg peak, R80, and Bragg peak FWHM comparisons for all commissioned IDD curves as a function of nominal beam energy. Differences are reported as a percentage of the measured value and average percent differences are displayed in parenthesis in the legend. (b) Overall 1D gamma pass rates for all commissioned energies using 1%/1 mm and 0.5%/0.5 mm evaluation criteria.

An SAD of 400 cm was determined to provide adequate spot size matching for all measurement planes and energies investigated. Figure 6 displays measured and simulated absolute (left) and relative (right) spot sizes with a 400-cm SAD. For the energies and planes investigated, all simulated and measured spot sizes agreed to within 4%. This agreement was deemed acceptable considering the 0.5 mm resolution of the Lynx and the uncertainty in the fit of the polynomial used to parameterize the sampled spot sizes at isocenter. Figure 7 illustrates the number of protons per MU that was calculated using Eq. (1). Simulations identical to the reference conditions described in TRS-398 were performed such that the uncertainty in the absorbed dose-to-water tally was all below 1%.

Fig. 6.

Measured and simulated absolute (left) and relative (right) spot sizes in X and Y for 85, 110, 130, and 160 MeV as a function of distance from isocenter. The downstream and upstream directions are indicated in the plot on the right.

Fig. 7.

Calculated output of TOPAS beam model in number of protons per MU for each of the nominal energies commissioned.

3.B. Off-axis beam model

Figure 8 displays the results for the 110 MeV measured and simulated beam spots at isocenter after the rigid optimization and Table II summarizes the agreement between the measured and simulated off-axis data for all energies at all measurement planes. Although the central beamlet is on-axis, it was still included in the analysis because the data used for on-axis commissioning were one-dimensional. For the energies and measurement planes investigated, the average median dose differences were less than 1% and the average 1%/1 mm gamma pass rates were all greater than 95% with a 1% dose threshold applied on evaluated points.

Fig. 8.

(a) Measured and simulated spot maps at isocenter for 110 MeV beamlets for on-axis and 5 cm deflected beamlets. Panels (b)–(d) measured and simulated line profiles taken along the X-direction through y = 50 mm (b), y = 0 mm (c), and y = −50 mm (d).

Table 2.

1%/1 mm gamma pass rates and median dose differences for 85, 110, and 160 MeV Lynx spot map measurements with a 1% dose threshold at all measurement planes.

Energy (MeV)	Isocenter + 100 mm	Isocenter	Isocenter − 100 mm	Average
1%/1 mm gamma pass rate (%), 1% dose threshold
85	89.1	98.1	98.6	95.3
110	95.9	99.2	99.9	98.3
160	99.8	98.4	99.8	99.
Median dose difference (%) [Meas. - MC], 1% dose threshold
85	−1.57	−0.92	−0.35	−0.95
110	−0.99	−1.10	−0.49	−0.86
160	−0.21	−0.12	0.05	−0.10

3.C. Range shifter characterization

Measured and simulated IDD curves were fit using a spline function to determine both the depth of the Bragg peak and the R80 for range shifted and pristine beams. For the 90, 125, and 165 MeV pristine beams, the measured and simulated depth of the Bragg peak and R80 was verified to within 0.17% and 0.08%, respectively. For their range shifted counterparts, the depth of the Bragg peak and R80 was verified to within 0.24% and 0.56%, respectively. This agreement was achieved through an optimization of the range shifter density, which was tuned to 0.96 g/cc (nominally ρ = 0.97 g/cc) to achieve the best overall agreement for the energies investigated. The measured and simulated WET of the polyethylene range shifter was determined to be 40.9 +/−0.1 and 41.0 +/−0.1 mm using the R80 pull-back method, respectively.

3.D. Collimated integral depth dose curves

Figures 9 and 10 display measured and simulated IDD curves for pristine and range shifted beam energies, respectively. For all the trimmer configurations outline in Table II, the average 1%/1 mm 1D gamma pass rates were 99.8% and 100% for the pristine and range shifted beams, respectively. However, when assessed at the 0.5%/0.5 mm criterion, the pristine and range shifted pass rates drop to 89.6% and 95.5%, respectively. This agreement is comparable to baseline model agreement reported in Section 3.A for the uncollimated commissioning measurements.

Fig. 9.

Measured and simulated pristine IDD curves for the 90 MeV beam trimmed by the X2 trimmer (top row) and the 125 MeV beam trimmed by the X2 and Y2 trimmers simultaneously (bottom row). Untrimmed IDDs are shown in blue to serve as reference IDDs to compare trimmed IDDs against. The figures in the left column provides an overall view of the IDD curve while the figures in right column are zoomed in to emphasize the differences in entrance dose resulting from collimation.

Fig. 10.

Measured and simulated range shifted IDD curves for the 125 MeV (RS) beam trimmed by the X2 trimmer (top row), the 125 MeV (RS) beam trimmed by the X2 and Y2 trimmers simultaneously (middle row), and the 165 MeV (RS) beam trimmed by the X2 trimmer. Untrimmed IDDs are shown in blue to serve as reference IDDs to compare trimmed IDDs against. The figures in the left column provides an overall view of the IDD curve while the figures in right column are zoomed in to emphasize the differences in entrance dose resulting from collimation.

3.E. Collimated lateral profiles

For all collimated profiles and beam energies investigated, a global 2D 1%/1 mm gamma test with a 1% dose threshold was used to evaluate the agreement between simulated and measured profiles. Figures 11–13 illustrate the measured and simulated 2D lateral profiles for the tightly collimated (only X2 shown), loosely collimated (only X2 shown), and double trimmed configurations for the range shifted beam energies investigated, respectively. Because a standardized 3 × 3 spot map was used for the Lynx measurements, the central spot’s dose profile for the range shifted 90 MeV profiles acquired at a depth of 10 mm exhibited small contributions from adjacent off-axis beamlets. These adjacent beamlet contributions are attributed to the larger σ_air at lower beam energies and additional spot size broadening due to range shifter and in-phantom scattering. To account for this, simulations for the range shifted 90 MeV beam mimicked the spot map delivery instead of the one, on-axis beamlet simulations that were performed for all other energies. For the range shifted beams and configurations investigated, the average 1%/1 mm pass rates were 99.1% at the surface and 99.8% at depth. For the pristine beams and configurations investigated, the average 1%/1 mm pass rates were 97.6% at the surface and 95.2% at depth.

Fig. 11.

Lynx measured (solid) and simulated profiles (dashed) for the “tightly” collimated trimmer configuration (X2 = 1 mm) for the range shifted 90, 125, and 165 MeV beams. Profiles measured in-air at isocenter are displayed in the top row while in-phantom profiles are displayed in the bottom row.

Fig. 13.

Lynx measured (solid) and simulated profiles (dashed) for beamlets collimated by the X2 and Y2 trimmers simultaneously for the range shifted 125 MeV beam. Profiles measured in-air at isocenter are displayed in the top row while in-phantom profiles are displayed in the bottom row.

4. DISCUSSION

This work presents a methodology for Monte Carlo-based modeling of a dynamic collimation system mounted to the IBA DN system. The beam model presented in this work has been benchmarked against IDD measurements as well as on- and off-axis spot size measurements at multiple planes in air. Verification in air helps ensure accurate representation of the beamlets, and thus accurate spot size, along the entire beam path. An SAD of 400 cm was determined through an optimization process such that the measured spot sizes agreed with the simulated spot sizes at multiple planes in air. The X and Y magnet-specific deflections were then incorporated downstream from the point source to ensure accurate modeling of beam deflection that is cohesive with the beamline optics and the DCS design, whose trimmers rotate about the magnet planes as they linearly translate to match the beam divergence.

The second portion of this work focused on the experimental validation of the proposed DCMC package. IDD curves and lateral profile measurements were acquired at MCI and compared to identical simulations for both pristine and range shifted beams for a variety of X, Y, and X & Y trimmer configurations. The WET of the polyethylene range shifter was measured to be 41.0 mm, which differs from the simulated WET by <0.4%. IDD curves and profiles were both analyzed with a 1D or 2D 1%/1 mm gamma test with a 1% dose threshold applied on all measured points. Excellent agreement was observed for all trimmed beams (both pristine and range shifted) with an average pass rate of 99.9% for the IDD curves and 97.9% for the lateral profiles. The worst agreement was observed for the range shifted and pristine 90 MeV beams; however, this agreement was comparable to both the model’s baseline agreement against commissioning measurements and uncollimated Lynx 2D profiles. We suspect this lack of agreement was due to the Gaussian-assumed energy spectra, and thus, exclusion of low-energy scatter originating in the beamline that subsequently undergoes large-angle scattering events that result in a more prominent nuclear halo.

The efforts made to create an accurate and experimentally validated DCMC model allow this model to be used in future investigations related to various aspects in treatment planning and dosimetry that must be addressed prior to clinical integration of the DCS. For example, this model could be used to evaluate the accuracy of the previously mentioned Hong aperture approximation currently implemented in many widely available TPSs. Due to the focused design of the DCS and inclusion of the polyethylene range shifter, it is hypothesized that a significant number of protons scattered in the range shifter may reduce the validity of a single aperture approximation and may require a more sophisticated approximation. Other future DCMC applications may include evaluation of heterogeneity corrections, accuracy of analytical algorithms in summation of high gradient spot edges, and advanced robustness analysis.

5. CONCLUSION

We have developed and validated a DCMC package specific to the DCS that consists of PBS source model, the DCS trimmers, and the polyethylene range shifter. The DCMC package has been published as an open-source package available for download here and consists of generic versions of the PBS source extension and trimmer extensions that were developed as a part of this work.

Fig. 12.

Lynx measured (solid) and simulated profiles (dashed) for the “loosely” collimated trimmer configuration (X2 = 3, 4, or 5 mm) for the range shifted 90, 125, and 165 MeV beams. Profiles measured in-air at isocenter are displayed in the top row while in-phantom profiles are displayed in the bottom row.

DATA AVAILABILITY STATEMENT

The Monte Carlo tools developed that support the findings of this study are openly available at http://doi.org/10.5281/zenodo.4088274. Additional documentation and usage instructions can be found at https://github.com/npnelson3/DynamicCollimationMonteCarloPackage.