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 D_99% for -10% and +10% errors was 0.7% and 1.1%, respectively. For -15% and +15% spot size errors, the average reduction in D_99% was 1.4% and 1.9%, respectively. The average reduction in D_99% 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 D_99% 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 D_99% was 0.8% (0.9%). For the spot size errors of ±10% and spot position errors of ±2 mm, the average reduction in D_99% 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 D_99% 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.

Keywords: Monte Carlo; SBRT; lung cancer; proton therapy; robust optimization; robustness; spot position; spot size.

Fig. 1

The average difference in clinical target volume D_95% (left panel) and D_99% (right panel) between simulated plans in Group 1 and nominal plans for the spot size errors (±10%, ±15%, and ±20%). The results are averaged over all five patients.

Fig. 2

Dose distributions in an example patient: (a) nominal plan, (b) simulated plan for the decreasing spot size (−10%) and spot position (+1 mm) evaluated simultaneously; (c) simulated plan for the increasing spot size (+10%) and spot position (+1 mm) evaluated simultaneously. The loss of target coverage in the simulated plans is shown by the red arrows on the right panel.

Fig. 3

The average difference in clinical target volume D_99% between simulated plans in Group 2 and nominal plans for the spot size errors (±10%) in conjunction with spot position errors (±1 and ±2 mm). The results are averaged over all five patients.

Fig. 4

(left panel) The average clinical target volume (CTV) D_99% (left panel) from 120 plans of five patients from Group 3 analysis. (right panel) The average difference in CTV D_99% between simulated plans in Group 3 and nominal plans. The results are averaged over all five patients.

Fig. 5

(left panel) The difference in clinical target volume homogeneity index (HI) for eight different scenarios between simulated plans in Group 3 and nominal plans. (right panel) Robustness parameters for eight scenarios of Group 3 analysis. The D(±10%, ±1 mm) plans are evaluated for setup (±5 mm) and range (±3.5%) uncertainties as described in Section 2.F.