An investigation into the robustness of dynamically collimated proton therapy treatments

Abstract

Purpose:

To investigate the dosimetric robustness of dynamically collimated proton therapy (DCPT) treatment plans delivered using a dynamic collimation system (DCS) with respect to random uncertainties in beam spot and collimator position as well as systematic offsets in the DCS mounting alignment. This work also demonstrates a technique that can increase plan robustness while preserving target conformity.

Methods:

Variability in beam spot and collimator positioning can result in changes to a beamlet’s dose distribution and incident fluence. The robustness of the DCPT treatment plans was evaluated for three intracranial treatment sites by modeling treatment variability as normally distributed random variables with standard deviations reflecting a clinical system. The simulated treatment plans were then recalculated and compared against their nominal, idealized dose distribution among several trials. It was hypothesized that a plan’s robustness to these delivery variables could be reduced by restricting a trimmer’s placement toward a beamlet’s central axis during collimation.

Results:

By introducing a minimum trimmer offset of 1.5 mm, the variation of the planning target volume (PTV) D_95% coverage was reduced to within 2% of the prescribed dose. The treatment plans with trimmers that were placed within 0.5 mm of a collimated beamlet’s central axis resulted in the greatest healthy tissue sparing but deviations as high as 11.4% to the PTV D_95% were observed. The nominal conformity of these treatment plans utilizing the 1.5 mm trimmer offset was also well maintained. For each treatment plan studied, the 90% conformity index remained within 6.25% of the conformity index achieved without a minimum trimmer offset, and the D_50% of surrounding healthy tissue increased by no more than 3.1 Gy relative to a plan without a trimmer offset.

Conclusions:

While DCPT can offer a significant reduction in healthy tissue irradiation, the results from this work indicate that special care must be taken to ensure proper PTV coverage amid uncertainties associated with this new treatment modality. A simple approach utilizing a minimum trimmer offset was able to preserve the majority of the target conformity and healthy tissue sparing the DCS technology affords while minimizing the uncertainties in this treatment approach.

1. INTRODUCTION

Dynamically collimated proton therapy (DCPT) is a derived form of pencil beam scanning (PBS) that makes use of a dynamic collimation system (DCS) to uniquely collimate each energy layer of the treatment.¹ Unlike a fixed aperture that is uniquely milled for each patient, the DCS effectively provides any aperture shape through the sequenced motion of two parallel sets of orthogonal trimmer blades. Recent treatment planning studies have indicated that DCPT with the DCS for intracranial targets can reduce the dose delivered to the 10-mm ring of healthy tissue immediately surrounding the planning target volume (PTV) by 13.7% and 8.5% compared to uncollimated and aperture-collimated treatments, respectively.^2–4 Head and neck treatments also showed a benefit with respect to OAR sparing.⁵ Recent work has indicated that the achievable target conformity can be further improved while also minimizing treatment delivery time through advancements in gradient descent and metaheuristic optimization techniques tailored specifically to the DCS technology.^6,7 However, the results from these studies were based on idealized dose distributions determined in the treatment planning system (TPS) and did not account for the potential influences from uncertainties unique to collimation in PBS proton therapy.

One potential variable that will impact the quality of DCPT treatment plans delivered with the DCS is spot placement. Any offset, stochastic or systematic, from the nominal setup will cause the individual collimated beamlet distributions to change. Table I lists a set of published beam spot offsets and other positioning uncertainties from literature. Variations in magnetic field strength may cause a nonuniform precision throughout the entire treatment field, and the accuracy of spot placement degrades further from the center of the field.⁸ Variability in the lateral beam spot placement, 0.5 mm systematically or up to 1.0 mm randomly, has been shown to result in 5% dose hot spots and a 3% decrease in PTV coverage volume.⁹ In a different study it was found that uniform fields with a lateral spacing of 3 and 6 mm were susceptible to 0.7% and 3.1% hot and cold spot pairs, respectively, per millimeter that a spot was misplaced.¹⁰

Table I.

Sources of treatment delivery variability summarized from literature that could impact dynamically collimated proton therapy treatments using a dynamic collimation system.

Component	Delivery system	Reported deviation	Measurement notes
Beam spot positioning8	IBA DN	±1.0 mm	25 × 25 cm2 field
Beam spot positioning8	IBA UN	±1.0 mm	25 × 25 cm2 field
Beam spot positioning8	IBA DN	±0.42 mm	Center of field
Beam spot positioning8	IBA UN	±0.42 mm	Center of field
Beam spot positioning11	Hitachi ProBeat	≤1.0 mm	20 × 20 cm2 field
Beam spot positioning10	Arbitrary scanning nozzle	1 mm–2 mm	Whole treatment
Beam spot positioning9	Hitachi ProBeat	0.5 mm maximum	Whole treatment
Beam spot positioning12	Hitachi ProBeat	96.76% coverage at 1 mm	Whole treatment
Trimmer positioning1	Precision stepper motor	±1 μm	Manufacturer tolerance

Estimates for spot positioning accuracy are provided for different pencil beam scanning systems including both the Universal Nozzle (UN) and Dedicated Nozzle (DN) systems from IBA.

The consequences of spot placement uncertainties are not well understood for DCPT and may be more complicated due to interplay. For instance, a small offset in either the beamlet or trimmer position while using the DCS can change the lateral distribution of the beamlet as shown in Fig. 1. Since the distribution of beam spots is a result of blocking a portion of the incident fluence, a change in the relative position between the trimmer blade and the beamlet’s central axis will also affect the fluence and relative dose contribution of the beam spot. Since DCPT provides energy-specific collimation, all collimated beamlets for each energy are subject to these combination of uncertainties with varying degrees of how they may impact the overall dose distribution.

Fig. 1.

Monte Carlo–simulated lateral proton beamlet distributions in the beam’s eye view resulting from collimation. Trimmer positions and corresponding dose distributions (no offset, left, 1.5 mm offset, right) are referenced from the origin, shown as a red dot, which coincides with the nominal spot position.

It is the primary focus of this work to investigate the robustness of DCPT treatments with respect to uncertainties associated with the beam line and collimation system. These include uncertainties in the dose delivery system’s spot positioning, the trimmer positioning accuracy of the DCS, and the overall mounting alignment between the dose delivery system and a DCS. It is hypothesized that small changes in beam spot and trimmer position have a large effect on fluence when trimmers are near the central axis of a proton beamlet. Therefore, the robustness of a DCPT treatment plan to positional uncertainties may be reduced by prohibiting the trimmers from being placed directly on a beamlet’s central axis.

2. MATERIALS AND METHODS

2.A. Nominal treatment planning

A set of three intracranial treatment plans from the works of Moignier et al.^2,4,5 and Smith et al.³ were replanned with an in-house TPS, RDX, using the asymmetric beamlet model for the IBA Universal Nozzle (UN) system.¹³ These plans included chordoma, ependymoma, and low-grade glioma treatment sites. An initial lateral and distal spot spacing of 4 and 5 mm, respectively, were used to place beam spots within a fixed grid about an expanded PTV. The spot positions, trimmer positions, spot grouping, and beamlet weights were optimized cohesively in order to maximize the healthy tissue sparing and target conformity while maintaining an estimated treatment time limit of approximately 60 s per treatment field to account for the sequencing of trimmer blades as beam spots are delivered.^6,7 An iterative optimization algorithm determines the position and orientation of trimmers for each beam spot to maximize the amount of healthy tissue and OAR sparing while maintaining the overall dose-volume histogram (DVH) goals throughout the composite plan’s weight optimization.

An additional hard constraint was placed on the off-axis collimator distance between the edge of the trimmer and the beamlet’s central axis. Since the magnitude of the minimum allowable trimmer offset could influence the resulting plan quality, several minimum offset distances were investigated including 0.5, 1.0, 1.5, and 2.0 mm. In the event that the trimmer position should move beyond the beamlet central axis due to the delivery variables incorporated into the nominal treatment plan, the beamlet distribution would be calculated as if the trimmer positions were along the beamlet’s central axis, which is the most extreme beamlet collimation defined in the asymmetric beamlet algorithm.¹³

2.B. Monte Carlo–determined fluence factors

The asymmetric beamlet algorithm is a model-based, dose-to-water pencil beam algorithm that was created by mathematically modeling the proton beamlet dose-to-water simulations in MCNPX using the following formalism,¹³

$$b\left(x,y,t,R\right)=D_T\left(t,R\right)\cdot O\left(x,y,t,T\right),$$ (1)

where the beamlet dose distribution, b, is calculated at each lateral coordinate (x,y) and radiological depth, t, within a medium of water with an expected range, R. The beamlet’s relative depth dose is described by a depth dose factor, D_T(t,R), that accounts for the elevated entrance dose due to low-energy scatter from the trimmer blade. Trimmer positions are defined at their respective medial edge positions, T ≡{X₁,X₂,Y₁,Y₂}, from the beamlet’s central axis. The depth dose factor is convolved with a lateral distribution function, O(x,y,t,T), that accounts for the asymmetric lateral spreading of the proton beamlet in water. To ensure the proper radial and depth dose distributions, the lateral component is normalized at all depths, t, by $\int {\int }_{-\infty }^{\infty }O\left(x,y,t,T\right)=1$. With the proper raytracing methods in place to determine radiological depth, the aforementioned formalism enables quick calculations of 3D beamlet dose distributions for PBS delivery with the DCS. However, changes in fluence with respect to the collimation are lost when beamlet distribution is normalized. An understanding between the change in fluence resulting from collimation and the resulting change in the maximum dose is necessary to relate the changes in beamlet intensity delivered to a specified machine output.

Dose distributions were simulated for nominal beamlet energies ranging from 97.6 to 184.2 MeV in MCNP6¹⁴ using a divergent point source modeled after the IBA UN nozzle system along with a model of the DCS. The model of the DCS was taken directly from the work of Gelover et al.¹³ and consisted of a 7.5 g/cm² thick graphite range shifter with a density of 2.1 g/cm³. The material defining the set of four collimation rods are modeled after a Ni-200 alloy with a density of 8.908 g/cm³. The change in the maximum dose at the Bragg peak due to changes in the trimmer positioning was quantitated using a Type 3 mesh tally. The resolution of the tally was set to the resolution used in the RDX TPS for all treatment plans investigated, 3 × 3 × 3 mm³, and spanned a lateral dimension of 6 × 6 cm². The maximum-value voxel within this array was taken to represent the result of the simulation. Simulations were executed with enough histories to achieve 1% simulation errors. For each nominal energy, trimmer arrangements in 5-mm increments extending as far out as 2.5 cm from the beamlet’s central axis were simulated. The results from these simulations were then parameterized through multiple regression in a script written in MATLAB® (R2017b) to derive an analytical model for fluence changes that would be used in the treatment planning robustness study.

2.C. Robustness study

Uncertainties in beam spot positioning, trimmer positioning, and DCS mounting alignment were treated as normally distributed random variables with a standard deviation estimated from the literature, which are summarized in Table II. Beam spot positioning was investigated using two different standard deviations of 0.25 and 0.5 mm. While some studies report a spot scanning accuracy of 1–2 mm,^8,10 this estimate is generally for the entire deliverable treatment field where the magnetic field homogeneity of the scanning magnets worsens as the angle of deflection widens. It was assumed that the beam spot positioning with a DCS may be better since treatments using the DCS are intended to be delivered within the central region of the dose delivery system. Some studies have shown that within the 25 × 25 cm² square region that the beam spot positioning accuracy can be within ±0.5 mm.^8–9,12 An estimate of mounting alignment was taken to be the quadrature sum of the work of Ciangaru et al.,¹⁵ and a conservative estimate was taken for trimmer positioning accuracy for a DCS. While the manufacturer-reported precision of the stepper motors is rather small, this estimate was expanded to account for other effects such as motor wear, backlash offset effects from all-day use, the degradation of the DCS track alignment over time, and the potential sag of the unit due to gravity. When applying these variations, the position of a trimmer is projected to the isocenter and then transformed to a coordinate system that is relative to the spot center when calculating the resulting beamlet dose distribution.

Table II.

List of treatment variables’ standard deviations assumed for beam spot position, trimmer position, and dynamic collimation system alignment estimated from the reported offsets listed in Table.

	Spot positioning	Trimmer positioning	Mounting alignment
Distribution	Stochastic (independent)	Stochastic (dependent)	Systematic (dependent)
Estimated σ1	0.25 & 0.50 mm	0.25 mm	0.25 mm

The robustness of three intracranial DCPT treatment plans was studied and is listed in Table III. Due to the probabilistic nature of the uncertainties investigated in his work, several trials were necessary to quantitate the potential changes that could occur from a nominal dose distribution. For this work, a trial is a single instance of a nominal treatment plan that has simulated at least one source of delivery variability. Trials that considered a composite of all three sources of delivery variability were completed in three steps. First, each beam spot was offset from its nominal position. Trimmer offsets were then applied across groups of beam spots that share a common set of trimmer positions. Finally, a shift in the entire DCS alignment from the patient CT coordinates was applied. The DCS alignment was treated as a deterministic, systematic shift that affects the trial as a whole. Once these shifts were applied during a trial, the plan was re-calculated applying the Monte Carlo-determined fluence corrections discussed in Section 2.B. Each trial was compared to the respective idealized planned dose distribution in terms of changes in target coverage and OAR dose. The metrics chosen for this work were the target conformity index, defined as the ratio of the prescription 90% or 50% isodose volumes to the PTV volume, the coverage index, defined as the ratio of the PTV volume receiving at least 90% of the prescription dose to the entire PTV volume, the homogeneity index (HI), defined as the difference in the PTV D_5% and D_95% normalized to the mean target dose, and DVH metrics including the D_2%, D_50%, and D_95% for the PTV and OARs.

Table III.

The delivery variables and minimum trimmer offsets studied for each treatment planning site.

Plan	Variables in delivery studied	Trimmer offset magnitudes (mm)
Chordoma	Spot/trimmer/mounting/composite	0.5, 1.0, 1.5, and 2.0
Ependymoma	Composite	1.0 and 1.5
Glioma	Composite	1.0 and 1.5

Simulated treatments that considered all three sources of variability are denoted as composite.

2.C.1. Specific investigations

An initial study was performed to isolate how each delivery variable could influence the nominal treatment plan. The chordoma treatment site was chosen for this initial study since it was expected that a smaller target would be more susceptible to uncertainties as it was composed of the fewest number of beam spots. During the first set of simulations, each delivery variable was modeled with a standard deviation of 0.25 mm so as to encapsulate 95% of the potential offsets to be within 0.50 mm. A second set of simulations were performed that were identical to the first set of simulations but with varying trimmer offset distances of 0.5, 1.0, 1.5, and 2.0 mm. Following this study, three separate treatment plans were investigated that included a composite of all three components of delivery variability and trimmer offsets of 1.0 and 1.5 mm. These simulations were performed with a spot positioning delivery variable modeled with a standard deviation of both 0.25 and 0.50 mm in order to investigate the effects of an expanded spot position uncertainty. Each of these studies utilized 100 trials per plan to quantitate the distribution of expected changes from the nominal coverage.

3. RESULTS

3.A. Monte Carlo–determined fluence factors

Absorbed dose-to-water simulations were performed for ten nominal therapeutic proton beamlet energies with various combinations of X- and Y-trimmer positions to study how the change in the nominal proton fluence would affect the dose near the Bragg peak. This is necessary to correct the beamlet weighting factors determined in RDX. All sets of simulations were normalized with respect to the maximum absorb dose-to-water value of an uncollimated proton beamlet with the same nominal proton beamlet energy.

For each energy, a 2D surface plot was fitted using MATLAB’s (version R2017b) linear least squares fitting algorithm. Increasing two-variable polynomial functions were used until the analytical model matched the Monte Carlo–simulated responses with an R² value of at least 0.99. The distributions from the polynomial model fitted using the response of the Monte Carlo simulations are shown in Fig. 2 for each energy.

Fig. 2.

(a) Fluence factor as a function of nominal beam energy and X- and Y-trimmer position for beam energies ranging between 97.6 MeV (up-most surface plot) and 184.2 MeV (bottom-most surface plot). (b) Fluence factor plot of the 97.6 MeV beam energy.

3.B. Specific investigations

Treatments were planned and optimized with trimmer offsets of 0.5, 1.0, 1.5, and 2.0 mm for the chordoma treatment plan, and 1.0 and 1.5 mm for the ependymoma and low-grade glioma plans. Figure 3 illustrates a DVH distribution optimized using a 1.5 mm minimum trimmer offset. The nominal DVH coverage is accompanied by 10 simulated dose distributions that have incorporated the treatment uncertainties investigated within this work.

Fig. 3.

Dose-volume histograms (DVH) for the chordoma treatment plan. The solid black lines represent the nominal DVH. The distribution of potential change is shown from the treatment delivery uncertainties listed in Table II modeling each parameter as a normally distributed random variable with a standard deviation of 0.25 mm.

The three components of robustness, listed in Table II, were simulated independently for the dual-field chordoma treatment planned with a 0.5 mm minimum off-axis trimmer distance. For this initial investigation, each of the uncertainties were normally distributed with a standard deviation of 0.25 mm. Changes in the dose coverage for the optic chiasm (D_50%,D_2%), brainstem (D_50%,D_2%), PTV (D_95%,D_2%), and 10-mm ring of surrounding healthy tissue (D_50%,D_2%) were monitored using absolute dose differences. The quality of the treatment plan was monitored using the metric of target homogeneity and reports the percent difference from the nominal plan. The upper and lower adjacent values of each distribution are plotted in Fig. 4 representing the 99.3% Z confidence interval range for the simulated cases.

Fig. 4.

Upper (positive) and lower (negative) adjacent values from 100 simulated treatment planning trials of the dual-field chordoma plan resulting from randomized offsets in beam spot positioning (gray), trimmer positioning (orange), and dynamic collimation system mounting alignment (blue). Dose-volume histogram metrics are shown for the optic chiasm, brainstem, 10-mm ring of surrounding healthy tissue, and the planning target volume along with changes in the nominal target homogeneity index (HI).

3.C. Trimmer offsets to enhance target coverage robustness

Four trimmer offsets were investigated with the dual field chordoma treatment plan. The simulated trials considered all three sources of uncertainty listed in Table II to determine the potential distribution in OAR and PTV coverage with each trimmer offset. The upper and lower adjacent values of the DVH metrics previously discussed are plotted in Fig. 5. It should be noted that the trials associated with the 0.5 mm minimum trimmer offset plan were susceptible to instances, by no more than a 12.3% chance, where the perturbed spot-trimmer configuration was outside the defined limits of the asymmetric beamlet model. These instances forced the calculation to stay within the defined limits of the asymmetric beamlet model. Thus, it may be the case that the magnitude of the lower adjacent values is underestimated for this case. The probability of this occurring was less than 1% for treatment plans optimized with a minimum off-axis trimmer distance of 1.0 mm or larger.

Fig. 5.

Upper (positive) and lower (negative) adjacent values from 100 simulated treatment planning trials of the dual-field chordoma treatment plan including all potential sources of treatment variability. Four optimized treatment plans of the chordoma site were considered resulting from a minimum off-axis trimmer distance of 0.5 mm (green), 1.0 mm (red), and 1.5 mm (purple), and 2.0 mm (black) from the beamlets’ central axes. Dose-volume histogram metrics are shown for the optic chasm, brainstem, 10-mm ring of surrounding healthy tissue, and the planning target volume.

The potential change in target coverage was based on the variability from the nominal PTV D_95% and D_2% DVH values. These metrics were used as a basis to estimate the amount of underdosing and overdosing resulting from the uncertainties evaluated in this work. The changes in target conformity are evaluated with respect to the nominal plan quality. Table IV lists the target coverage, conformity, and homogeneity indices for each of the three treatment plans optimized with trimmer offsets of 1.0 and 1.5 mm.

Table IV.

Treatment planning metrics for the nominal chordoma, ependymoma, and glioma treatment plans optimized with trimmer offsets ranging from 0.0 to 2.0 mm.

				Conformity
Plan	Offset (mm)	HI	CI	90%	50%	NT Ring D50% (Gy)
Chordoma	0.0	0.13	0.99	1.75	3.52	38.29
	0.5	0.13	0.99	1.77	3.59	38.90
	1.0	0.14	1.00	1.78	3.59	38.93
	1.5	0.13	1.00	1.77	3.64	39.08
	2.0	0.13	1.00	1.78	3.68	39.39
Ependymoma	0.0	0.13	0.99	1.41	2.03	41.45
	1.0	0.14	0.98	1.45	2.21	43.94
	1.5	0.13	0.98	1.46	2.20	44.03
Glioma	0.0	0.17	0.98	1.55	2.60	39.58
	1.0	0.15	0.98	1.59	2.71	41.61
	1.5	0.15	0.98	1.65	2.77	42.72

Each plan was evaluated and compared with respect to its target homogeneity index (HI), coverage index (CI), 90% and 50% conformity index, and median dose to the 10 mm ring of healthy tissue.

The robustness analysis among the three treatment plans optimized with a 1.0 and 1.5 mm minimum trimmer offset was repeated with a larger value for the spot positioning uncertainty distribution. The nominal standard deviation assumed for the spot displacement random variable was increased from 0.25 to 0.50 mm to investigate the potential consequences in plan robustness resulting from a larger spot position uncertainty of the scanning system. The upper and lower adjacent values in each distribution are plotted in Fig. 6 in comparison to the same plans simulated with the smaller spot positioning variability.

Fig. 6.

The resulting distribution of planning target volume D_95% coverage and maximum dose, D_2%, for the chordoma, ependymoma, and glioma treatment plans. Baseline treatment plans were either optimized with a minimum trimmer offset of 1.0 mm (top row) or 1.5 mm (bottom row). A total of 100 simulated treatment plans were calculated based on the delivery variables listed in Table II and characterized using a normally distributed random variable with a standard deviation of 0.25 mm.

4. DISCUSSION

4.A. Considerations of delivery variables with a dynamic collimation system

Changes in the primary proton fluence dominate the overall change in a beamlet’s absolute dose distribution. This is a subsidiary result from the Monte Carlo–determined fluence factor investigation. As shown in Fig. 2, the change in the observed maximum dose at the Bragg peak drastically increases as the trimmer approaches the beamlet’s central axis. Since the fluence of a proton beamlet is greatest at its center, the changes in collimation near the central axis will have the greatest influence on the spot intensity. This effect has a subtle geometric dependence between the X- and Y-trimmer blades; the X-trimmer in the DCS is positioned more distal towards the patient surface than the Y-trimmer. Geometrically, the Y-trimmer will cover a larger angular displacement from a focal point per distance translated from the central axis than the X-trimmer. Therefore, the rate of change and magnitude of change in the beamlet’s point of maximum dose is larger for the Y-trimmer. Additionally, these single beamlet dose trends suggest that a plan is more susceptible to the PTV being underdosed than overdosed since the gradient of change in the beamlet’s intensity as a function of trimmer offset increases toward the central axis.

4.B. Treatment planning robustness study

Several robustness studies were performed based on the uncertainties associated with a DCPT treatment plan. Initially, the components of treatment uncertainty were isolated for each component and modeled as a normally distributed random variable. As shown in Fig. 4, a systematic shift in the DCS alignment was found to have the largest influence on an entire treatment plan than either random variations in beam spot or trimmer positioning. For the DCPT chordoma treatment plan summarized in Fig. 4, an uncertainty in spot position with a standard deviation of 0.25 mm resulted in reductions to the PTV D_95% by 1.34% and increased D_2% hotspots by 1.37% of the prescribed dose. This is similar to what was reported for uncollimated treatment plans with similar spot spacing as shown from the treatment planning study of spot position variability reported from Yu et al.¹⁰

It was determined that a minimum off-axis trimmer distance between 1.0 and 1.5 mm could provide adequate target coverage robustness while maintaining a high degree of target conformity relative to uncollimated treatments in the presence of spot positioning variability for the IBA UN beamline model studied in this work. This was assessed by evaluating the robustness of two additional intracranial treatments planned with minimum allowable off-axis trimmer positions of 1.0 and 1.5 mm. While increasing the trimmer offset provides a more robust plan to these uncertainties, it also leads to a less conformal plan. Trimmer offsets larger than 1.0 mm preserved the PTV D_95% to within 2% of the prescribed dose and the benefits of added offset distance diminished at an offset distance of 2.0 mm indicating that beam spot positioning was becoming the dominant factor in the plan robustness. While these trimmer offsets appear to be well suited for the IBA UN beamline, they are most likely not generalizable. The spot size of a PBS system will change the off-axis fluence characteristics as characterized in the Monte Carlo section of this work. For example, a 1.5 mm trimmer offset would offer less collimation when combined with the IBA DN system given its small spot size in comparison to the IBA UN system.

The robustness of the optimized treatment plans using a 1.0 and 1.5-mm trimmer offsets was further investigated with the ependymoma and low-grade glioma treatment plans. These additional plans were investigated to check the generality of a single trimmer offset to increase the planned PTV coverage robustness with regard to different distributions of nominal beam energies, patient geometry, and PTV size. The distribution of these simulated changes in PTV coverage is shown in the box plots in Fig. 6. The range of simulated target coverage deviations among the three plans for 1.0 and 1.5 mm trimmer offsets evaluated are listed in Table V. Among the three treatment plans studied in this work, a 1.5 mm trimmer offset was shown to maintain a PTV D_95% coverage to within ±2% within a 99.3% confidence interval of the prescribed value while in the presence of all uncertainties studied. As much as a 4.7% difference was noticed when a 1.0 mm trimmer offset was applied with a spot positioning standard deviation of 0.50 mm.

Table V.

Results from the studies investigating the influence of delivery variability in spot positioning, trimmer positioning, dynamic collimation system mounting alignment, and minimum trimmer offset distance on the treatment plan robustness of a dual-field chordoma, ependymoma, and low-grade glioma treatment plan.

Treatment Plan	Minimum allowed Trimmer offset (mm)	Spot positioning Uncert. σ (mm)	Max overdose (% of prescribed)	Min underdose (% of prescribed)	Max underdose (% of prescribed)
Chordoma	1.5	0.25	0.66	1.47	4.8
Ependymoma	1.5	0.25	0.56	0.52	3.0
Low-grade Glioma	1.5	0.25	0.37	1.02	3.8
	Average		0.53 (0.12)	1.00 (0.39)	3.8 (0.7)
Chordoma	1.0	0.25	0.93	3.00	4.6
Ependymoma	1.0	0.25	1.00	1.26	3.3
Low-grade Glioma	1.0	0.25	0.71	1.32	4.3
	Average		0.88 (0.12)	1.86 (0.81)	4.1 (0.6)
Chordoma	1.5	0.50	1.34	2.47	6.1
Ependymoma	1.5	0.50	0.84	1.24	3.8
Low-grade Glioma	1.5	0.50	0.74	1.73	4.9
	Average		0.97 (0.26)	1.81 (0.51)	4.9 (0.9)
Chordoma	1.0	0.50	1.00	3.20	6.6
Ependymoma	1.0	0.50	1.33	2.93	4.3
Low-grade Glioma	1.0	0.50	0.39	4.67	5.1
	Average		0.91 (0.39)	3.6 (0.76)	5.3 (0.95)

The average and standard deviation in paranthesis are shown below each group.

5. CONCLUSIONS

The robustness of PBS proton therapy treatments delivered with a DCS was investigated in this work. A set of three nominal intracranial treatment plans were studied to investigate how delivery variability in beam spot positioning, DCS trimmer positioning, and DCS mounting alignment could manifest toward a degradation in the overall target coverage. Individual components of treatment uncertainty unique to treatments using a DCS were isolated, which the DCS mounting alignment was found to have the strongest influence on the plan robustness followed by the variable of beam spot positioning. The greatest changes to a beamlet’s dose distribution occurred when the trimmers are nominally close to the beamlet’s central axis. Therefore, the overall tendency of a DCPT treatment plan, given the treatment delivery variables presented, tend toward an under dosing of the target. Thus, it was determined that by instituting a minimum allowable off-axis trimmer distance the plan could be made more robust at the cost of slightly reducing the maximum achievable target conformity. A conservative off-axis trimmer distance between 1.0 to 1.5 mm was determined from this study to afford an adequate balance of increased plan robustness towards the aforementioned treatment delivery variables while still maintaining a high degree of target conformity.