Robust Optimization for Spot Scanning Proton Therapy based on Dose-Linear Energy Transfer (LET) Volume Constraints

Purpose: Historically, spot scanning proton therapy (SSPT) treatment planning utilizes dose volume constraints and linear-energy-transfer (LET) volume constraints separately to balance tumor control and organs-at-risk (OARs) protection. We propose a novel dose-LET volume constraint (DLVC)-based robust optimization (DLVCRO) method for SSPT in treating prostate cancer to obtain a desirable joint dose and LET distribution to minimize adverse events (AEs). Methods: DLVCRO treats DLVC as soft constraints controlling the joint distribution of dose and LET. Ten prostate cancer patients were included with rectum and bladder as OARs. DLVCRO was compared with the conventional robust optimization (RO) method using the worst-case analysis method. Besides the dose-volume histogram (DVH) indices, the analogous LETVH and extra-biological-dose (xBD)-volume histogram indices were also used. The Wilcoxon signed rank test was used to measure statistical significance. Results: In nominal scenario, DLVCRO significantly improved dose, LET and xBD distributions to protect OARs (rectum: V70Gy: 3.07\% vs. 2.90\%, p = .0063, RO vs. DLVCRO; $\text{LET}_{\max}$ (keV/um): 11.53 vs. 9.44, p = .0101; $\text{xBD}_{\max}$ (Gy$\cdot$keV/um): 420.55 vs. 398.79, p = .0086; bladder: V65Gy: 4.82\% vs. 4.61\%, p = .0032; $\text{LET}_{\max}$ 8.97 vs. 7.51, p = .0047; $\text{xBD}_{\max}$ 490.11 vs. 476.71, p = .0641). The physical dose distributions in targets are comparable (D2%: 98.57\% vs. 98.39\%; p = .0805; CTV D2% - D98%: 7.10\% vs. 7.75\%, p = .4624). In the worst-case scenario, DLVCRO robustly enhanced OAR while maintaining the similar plan robustness in target dose coverage and homogeneity. Conclusion: DLVCRO upgrades 2D DVH-based to 3D DLVH-based treatment planning to adjust dose/LET distributions simultaneously and robustly. DLVCRO is potentially a powerful tool to improve patient outcomes in SSPT.