A single-field-each-peak optimization method for motion-robust proton LATTICE therapy

LATTICE therapy delivers a spatially modulated dose pattern of high-dose peaks and low-dose valleys to the tumor target. Traditionally, LATTICE treatments have been implemented using photon beams; however, recent advancements have enabled the development of proton LATTICE (pLATTICE). Conventional pLATTICE planning typically relies on the convergence of multiple beam angles to form each high-dose peak, rendering peak localization highly sensitive to delivery uncertainties. These uncertainties include respiratory motion, proton range uncertainty, and intra-fraction anatomical variations, which can disrupt the geometric alignment of beams and compromise the spatial accuracy of peak deposition.

To address these challenges, we propose a novel single-field-each-peak (SFEP) optimization framework for robust pLATTICE delivery, during which the optimization method imposes that each peak is delivered using exactly one field. By avoiding multi-field convergence at individual peaks, the proposed approach aims to improve robustness against motion, range uncertainty, and anatomical variation while preserving the spatially fractionated dose pattern characteristic of LATTICE therapy.

The SFEP optimization approach enhances the motion robustness of pLATTICE by assigning each lattice vertex (peak) to a single field (beam angle) selected from a set of candidates beam orientations. This is achieved by defining SFEP as a mixed integer optimization problem in which the binary variables assign a single field to each peak (from a set of candidate fields), while continuous variables optimize proton spot weights. The optimization method simultaneously determines the field selection and proton spot weights, where the solution is obtained through a combination of alternating direction method of multipliers and iterative convex relaxation techniques.

The proposed method (NEW) was validated against the exhaustive search (ES) approach, in which beam angles for each peak were preselected and fixed without optimization. NEW consistently delivered each peak using a single field, while maintaining comparable peak-to-valley dose ratio (PVDR) and conformity index (CI). Robustness of the SFEP method was evaluated under standard 3.5% range and 5 mm setup uncertainties, and demonstrated superior robustness compared to intensity-modulated proton therapy (IMPT)-based pLATTICE. Additionally, motion-robust evaluation was performed using simulated directional shifts to mimic patient or anatomical motion. In the abdomen case, shifts of [-3, -3, 3] at field one, [3, 3, -3] at field two, and [-3, 3, -3] at field three were applied. Compared to IMPT, SFEP maintained more stable peak localization and coverage; for example, peak coverage at the 100% prescription dose decreased from 100% to 82.5% in SFEP after the shifts, versus 89.5% to 64.6% in IMPT.

This study introduces a novel SFEP optimization approach for achieving motion-robust pLATTICE, in which each peak is delivered using a single optimally chosen field. The SFEP method successfully delivers each peak with a single field while maintaining plan quality compared to exhaustive search (ES) plans and demonstrates superior robustness in peak localization and coverage compared to IMPT.