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 that control the shapes of the dose-LET volume histogram (DLVH) curves. It minimizes the overlap of high LET and high dose in OARs and redistributes high LET from OARs to targets in a user defined way. Ten prostate cancer patients were included in this retrospective study. Rectum and bladder were considered as OARs. DLVCRO was compared with the conventional robust optimization (RO) method. Plan robustness was quantified using the worst-case analysis method. Besides the dose-volume histogram (DVH) indices, the analogous LET-volume histogram (LETVH), extra-biological-dose (the product of per voxel dose and LET)-volume histogram (xBDVH) indices characterizing the joint dose/LET distributions and DLVH indices were also used. The Wilcoxon signed rank test was performed to measure statistical significance.

Results: In the nominal scenario, DLVCRO significantly improved joint distribution of dose and LET to protect OARs compared with RO. The physical dose distributions in targets and OARs are comparable. In the worst-case scenario, DLVCRO markedly enhanced OAR protection (more robust) while maintaining almost the same 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.