Impact of errors in spot size and spot position in robustly optimized pencil beam scanning proton‐based stereotactic body radiation therapy (SBRT) lung plans

Abstract Purpose The purpose of the current study was threefold: (a) investigate the impact of the variations (errors) in spot sizes in robustly optimized pencil beam scanning (PBS) proton‐based stereotactic body radiation therapy (SBRT) lung plans, (b) evaluate the impact of spot sizes and position errors simultaneously, and (c) assess the overall effect of spot size and position errors occurring simultaneously in conjunction with either setup or range errors. Methods In this retrospective study, computed tomography (CT) data set of five lung patients was selected. Treatment plans were regenerated for a total dose of 5000 cGy(RBE) in 5 fractions using a single‐field optimization (SFO) technique. Monte Carlo was used for the plan optimization and final dose calculations. Nominal plans were normalized such that 99% of the clinical target volume (CTV) received the prescription dose. The analysis was divided into three groups. Group 1: The increasing and decreasing spot sizes were evaluated for ±10%, ±15%, and ±20% errors. Group 2: Errors in spot size and spot positions were evaluated simultaneously (spot size: ±10%; spot position: ±1 and ±2 mm). Group 3: Simulated plans from Group 2 were evaluated for the setup (±5 mm) and range (±3.5%) errors. Results Group 1: For the spot size errors of ±10%, the average reduction in D99% for −10% and +10% errors was 0.7% and 1.1%, respectively. For −15% and +15% spot size errors, the average reduction in D99% was 1.4% and 1.9%, respectively. The average reduction in D99% was 2.1% for −20% error and 2.8% for +20% error. The hot spot evaluation showed that, for the same magnitude of error, the decreasing spot sizes resulted in a positive difference (hotter plan) when compared with the increasing spot sizes. Group 2: For a 10% increase in spot size in conjunction with a −1 mm (+1 mm) shift in spot position, the average reduction in D99% was 1.5% (1.8%). For a 10% decrease in spot size in conjunction with a −1 mm (+1 mm) shift in spot position, the reduction in D99% was 0.8% (0.9%). For the spot size errors of ±10% and spot position errors of ±2 mm, the average reduction in D99% was 2.4%. Group 3: Based on the results from 160 plans (4 plans for spot size [±10%] and position [±1 mm] errors × 8 scenarios × 5 patients), the average D99% was 4748 cGy(RBE) with the average reduction of 5.0%. The isocentric shift in the superior–inferior direction yielded the least homogenous dose distributions inside the target volume. Conclusion The increasing spot sizes resulted in decreased target coverage and dose homogeneity. Similarly, the decreasing spot sizes led to a loss of target coverage, overdosage, and degradation of dose homogeneity. The addition of spot size and position errors to plan robustness parameters (setup and range uncertainties) increased the target coverage loss and decreased the dose homogeneity.

superior-inferior direction yielded the least homogenous dose distributions inside the target volume.

Conclusion:
The increasing spot sizes resulted in decreased target coverage and dose homogeneity. Similarly, the decreasing spot sizes led to a loss of target coverage, overdosage, and degradation of dose homogeneity. The addition of spot size and position errors to plan robustness parameters (setup and range uncertainties) increased the target coverage loss and decreased the dose homogeneity.

| INTRODUCTION
In pencil beam scanning (PBS) proton delivery, the accuracy of the size and position of a pencil proton beam is very critical to minimize the discrepancies between the delivered and computed doses. Spot sizes on the proton beam delivery system can be affected by the fluctuations in the beam extraction and transport systems. 1 Additionally, the presence of different scattering materials in the nozzle, 1 as well as the air gap between the range shifter and patient, can have an impact on the spot size. 2 Similarly, the positioning of the spots can be affected by the fluctuations in the steering magnetic fields. 3,4 Hence, the variations in the delivered spot sizes and positions could lead to perturbation of dose distributions impacting the quality of the treatment plan delivered to the patient. [1][2][3][4][5][6][7] In order to minimize the discrepancies between the computed and delivered dose distributions in PBS proton therapy, tolerance levels are proposed for the spot size and position errors. Parodi et al. 1  Based on their gamma analysis, the spot size tolerance of AE10% was proposed. 8 Kraan and colleagues 7 demonstrated that the variation in spot size is patient and spot width dependent. Their study 7 included seven patients of different disease sites (pelvis, chest wall, rectum, chordoma, cardiac, retro-peritoneal, and sarcoma) and a phantom. If in-air one sigma (σ) of a pencil beam is 2.5 mm, the tolerance is AE25%. 7 Similarly, for σ of 5 and 10 mm, the proposed tolerances are AE25% and AE10%, respectively. 7 For the spot position errors, the tolerance of AE1 mm has been reported by the investigators. 4,[8][9][10] Recently, the AAPM TG224 report 11 recommended the tolerance of AE10% for the spot size and AE1 mm for the spot position.
Previous publications [1][2][3][4][5][6][7][8][9] have reported the variations in spot size and position in the phantoms and disease sites but not for the lung. For PBS lung cancer treatment, the accuracy of the dose calculation algorithm in predicting spot size and dose distributions becomes more critical due to varying tissue densities in the proton beam path. In commercial proton treatment planning systems (TPS), Monte Carlo algorithms have been shown to be more accurate in estimating spot sizes than analytical pencil beam algorithms. 12,13 A growing number of publi-  19,20 The in-air one sigma (σ) for 226.5 MeV at the isocenter is~3 mm. 19 For each patient, a nominal plan was regenerated for a total dose of 5000 cGy(RBE) in 5 fractions using an average RBE of 1.1. Treatment plans were robustly optimized using a single-field optimization (SFO) technique. The Monte Carlo algorithm (10 000 ions/spot) was utilized for the robust optimization.
The robustness (range uncertainty = AE3.5% and setup error = AE5 mm) was applied on the CTV such that its 99% of the relative volume receives at least the prescription dose (5000 cGy(RBE)).
Based on the input values of robustness parameters, RayStation optimized each plan for a total of 21 scenarios. The final dose calculations were performed using the Monte Carlo (grid size: 2 mm; statistical uncertainty = 0.5%). This was followed by the creation of a volumetric repainting plan with five paintings in an alternating order. 21,22 The resulting plan was then normalized such that the CTV D 99% = 5000 cGy(RBE). The final nominal plan was denoted as D(0%, 0 mm), which means 0% error in spot size and 0-mm error in spot position.

2.B | Spot size errors simulation
In order to simulate the spot size errors of AE10%, AE15%, and AE20%, additional six beam models were generated. These were simulated by scaling the spot profiles in the nominal beam model. In the simulated beam models, absolute dose output and integrated depth doses (IDDs) remained identical as in the nominal beam model.

2.C | Dose calculations for spot size errors only
The spot size errors calculation was performed by recomputing D (0%, 0 mm) plan using the simulated beam models (AE10%, AE15%, and AE20%). For instance, if D(0%, 0 mm) plan was recomputed for the spot size error of +10% and spot position error of 0 mm, the resulting plan was denoted as D(+10%, 0 mm). Similarly, for −20% spot size and 0-mm spot position errors, the plan was denoted as D(−20%, 0 mm). Dose recomputations were performed using the Monte Carlo algorithm without plan reoptimization.

2.D | Spot position errors simulation
The D(0%, 0 mm) plan containing the spot position information was exported from the TPS to a local computer. Then spot positions in the treatment plan were varied systematically by −1 and +1 mm, thus resulting in two simulated plans, D(0%, −1 mm) and D(0%, +1 mm), respectively. This process was repeated for the systematic for AE10% spot size errors.

2.F | Robustness
The D(AE10%, AE1 mm) plans were evaluated for a total of eight scenarios. The setup uncertainty was simulated by a 5-mm isocenter shift in the left-right, superior-inferior, and anterior-posterior directions of the patient resulting in six scenarios. The range uncertainty was evaluated for two scenarios (AE3.5%).

2.G | Analysis
The analysis was divided into three groups. The first group (Group 1) consisted of plans simulated for spot size errors only, as described in  The difference was averaged (Δ avg ) over five patients.
The CTV dose homogeneity index (HI) was evaluated using Eq. The loss of target coverage in the simulated plans is shown by the red arrows on the right panel.
where Rx is the prescription dose (5000 cGy(RBE)). Based on Eq. (3), the HI value of 0 is considered an ideal HI result.

3.A | Group 1: Spot size errors
The spot size errors resulted in a loss of the target coverage (Fig. 1).
The reduction in target coverage increased as the magnitude of spot size error was increased.

ACKNOWLEDG MENTS
The authors would like to thank Dr. Noufal Manthala Padannayil (Apollo Proton Cancer Centre, Chennai, Tamil Nadu, India) for his assistance with spot position errors simulation.

CONFLI CT OF INTEREST
The authors do not have any relevant conflict of interest to disclose.

D A T A A V A I L A B I L I T Y S T A T E M E N T
The data that support the findings of this study are available from the corresponding author upon reasonable request.