Impact of robust optimization and beam configuration on the distribution stability of LET under delivery uncertainties in carbon‐ion therapy

BACKGROUND: Carbon-ion radiotherapy exploits high linear energy transfer (LET) to enhance biological effectiveness, and low dose-averaged LET (LETd) within the target volume is associated with local recurrence in pancreatic cancer. Although robust optimization is widely used to improve dose robustness against delivery uncertainties, systematic investigation of LET robustness across optimization strategies and beam configurations remains scarce. PURPOSE: To evaluate the robustness of LET metrics in carbon-ion therapy under delivery uncertainties using a phantom-based design, comparing planning target volume (PTV)-based with robust optimization and assessing the impact of seven beam configurations, and to characterize the differential response of LET and clinical dose (relative biological effectiveness [RBE]-weighted dose) metrics. METHODS: water-equivalent phantom with rod- and C-shaped target geometries was planned in RayStation 12A with 50 Gy (RBE) in 10 fractions. Section 1 used two opposing lateral fields to compare PTV-based optimization (1, 3, 5 mm margins) with robust optimization incorporating translation, density, and combined uncertainties. Section 2 evaluated seven beam configurations, ranging from two-field to four-field arrangements, under PTV-based (3 mm) and robust (± 3%/3 mm) optimization. LETd98%, LETd mean, and LETd2% were extracted for the clinical target volume and organs at risk (OARs). Robustness was quantified using averaged interquartile range (AVG.IQR) and sensitivity slopes from 1% to 5% density uncertainty (S1→5), and configurations were ranked by minimal-change and biologically favorable criteria. Spot weight distributions were analyzed to examine the mechanistic basis of the observed differences. RESULTS: Density-related uncertainties dominated LET variability, with LETd2% the most sensitive metric (AVG.IQR up to 40% for C-shaped targets). Robust optimization with combined translation-density parameters achieved lower variability than PTV-based optimization. LET and RBE-weighted dose metrics responded divergently, with the LETd mean increasing while the mean clinical dose decreased under density perturbations. Beam direction significantly affected LETd2% variability (p < 0.001 for all configurations). Two lateral fields (2Lat) ranked highest under the minimal-change criterion, whereas four-field oblique (4FO) with robust optimization ranked first under the biologically favorable criterion, balancing increased target LET against reduced OAR exposure. Spot weight analysis showed that, for the rod-shaped target, only robustness scenarios including density uncertainty used more energy layers and shifted weight away from distal layers (distal-third weight fraction 56.4-57.4% vs. 60.8% for PTV-based optimization); this pattern was not reproduced for the C-shaped target. CONCLUSIONS: Density uncertainties predominantly govern LET variability in carbon-ion therapy, with LETd2% the most sensitive indicator, and redistribution of spot weight away from distal energy layers provides a plausible mechanism. Beam configuration selection should reflect clinical priorities: 4FO with robust optimization when biological effectiveness is prioritized, and 2Lat for physical LET stability. These phantom-based findings support explicit LET robustness evaluation in carbon-ion treatment planning and warrant validation in patient studies.