A Single-Field-Each-Peak Optimization Method for Motion-Robust Proton Lattice Therapy
Abstract
Purpose
Proton LATTICE (pLATTICE) therapy delivers spatially heterogeneous dose distributions with high‑dose peaks embedded within low‑dose valleys. Conventional pLATTICE planning typically uses multiple beam angles per peak, making peak localization vulnerable to proton range uncertainty and intra‑fractional motion. These uncertainties can degrade spatial accuracy and shift peaks away from intended tumor sub‑volumes. This study proposes a single‑field‑each‑peak (SFEP) optimization framework designed to reduce motion sensitivity by delivering each peak with a single, optimally selected beam angle.
Methods
In the SFEP framework, each lattice vertex (peak) is assigned to one field selected from a predefined set of candidate beam orientations. The resulting optimization problem is formulated as a mixed‑integer model in which binary variables determine peak‑to‑field assignment and continuous variables optimize proton spot weights. Field selection and spot‑weight optimization are solved simultaneously using an alternating direction method of multipliers combined with iterative convex relaxation.
Results
The SFEP framework generated proton LATTICE plans in which each high‑dose peak was delivered by a single, automatically selected field. Across all evaluated cases, SFEP achieved spatial peak placement and peak‑to‑valley dose characteristics comparable to exhaustive‑search assignments. Under robustness testing with 3.5% range and 5 mm setup uncertainties, SFEP demonstrated greater stability than IMPT‑based pLATTICE, showing smaller variations in peak dose and localization. Motion‑shift simulations further highlighted this advantage: in the abdominal case, SFEP preserved peak geometry and coverage with less degradation than IMPT. Peak coverage at the prescription dose decreased from 100% to 82.5% with SFEP, whereas IMPT showed a larger decline from 89.5% to 64.6%. Overall, SFEP maintained peak fidelity and target coverage under both uncertainty and motion conditions.
Conclusion
The SFEP optimization framework enables motion‑robust proton LATTICE planning by delivering each peak with a single optimally chosen beam angle while maintaining plan quality and improving robustness in peak localization and target coverage.