Technical Note: 4D robust optimization in small spot intensity-modulated proton therapy (IMPT) for distal esophageal carcinoma

Abstract

Purpose: To compare the dosimetric performances of small-spot three-dimensional (3D) and four-dimensional (4D) robustly optimized intensity-modulated proton (IMPT) plans in the presence of uncertainties and interplay effect simultaneously for distal esophageal carcinoma.

Method and materials: Thirteen (13) patients were selected and re-planned with small-spot ( $\sigma$ ~ 2-6 mm) 3D and 4D robust optimization in IMPT, respectively. The internal clinical target volumes (CTV_high3d , CTV_low3d ) were used in 3D robust optimization. Different CTVs (CTV_high4d , CTV_low4d ) were generated by subtracting an inner margin of the motion amplitudes in three cardinal directions from the internal CTVs and used in 4D robust optimization. All patients were prescribed the same dose to CTVs (50 Gy[RBE] for CTV_high3d /CTV_high4d and 45 Gy[RBE] for CTV_low3d /CTV_low4d ). Dose-volume histogram (DVH) indices were calculated to assess plan quality. Comprehensive plan robustness evaluations that consisted of 300 perturbed scenarios (10 different motion patterns to consider irregular motion (sampled from a Gaussian distribution) and 30 different uncertainties scenarios (sampled from a 4D uniform distribution) combined), were performed to quantify robustness to uncertainties and interplay effect simultaneously. Wilcoxon signed-rank test was used for statistical analysis.

Results: Compared to 3D robustly optimized plans, 4D robustly optimized plans had statistically improved target coverage and better sparing of lungs and heart (heart D_mean , P = 0.001; heart V_30Gy[RBE] , P = 0.001) in the nominal scenario. 4D robustly optimized plans had better robustness in target dose coverage (CTV_high4d V_100% , P = 0.002) and the protection of lungs and heart (heart D_mean , P = 0.001; heart V_30Gy[RBE] , P = 0.001) when uncertainties and interplay effect were considered simultaneously.

Conclusions: Even with small spots in IMPT, 4D robust optimization outperformed 3D robust optimization in terms of normal tissue protection and robustness to uncertainties and interplay effect simultaneously. Our findings support the use of 4D robust optimization to treat distal esophageal carcinoma with small spots in IMPT.

Keywords: 4D robust optimization; distal esophageal carcinoma; intensity-modulated proton therapy; interplay effect; small spots.