AbstractBackgroundLATTICE radiation therapy delivers 3D heterogenous dose of high peak‐to‐valley dose ratio (PVDR) to the tumor target, with peak dose at lattice vertices inside the target and valley dose for the rest of the target. Although the lattice vertex positions can impact PVDR inside the target and sparing of organs‐at‐risk (OAR), they are fixed as constants and not optimized during treatment planning in current clinical practice.PurposeThis work proposes a new LATTICE plan optimization method that can optimize lattice vertex positions during LATTICE treatment planning, which is the first lattice position optimization study to the best of our knowledge.MethodsThe new LATTICE treatment planning method optimizes lattice vertex positions as well as other plan variables (e.g., photon fluences or proton spot weights), with optimization objectives for target PVDR and OAR sparing. To satisfy mathematical differentiability, the lattice vertices are approximated in sigmoid functions. For geometric feasibility, proper geometry constraints are enforced onto lattice vertex positions. The lattice position optimization problem is solved by iterative convex relaxation (ICR) method and alternating direction method of multipliers (ADMM), and lattice vertex positions and photon/proton plan variables are jointly updated via the Quasi‐Newton method.ResultsBoth photon and proton LATTICE RT were considered, and the optimal lattice vertex positions in terms of plan objectives were found by solving all possible combinations on given discrete positions via exhaustive searching based on standard IMRT/IMPT, which served as the ground truth for validating the new LATTICE method. The results show that the new method indeed provided the optimal lattice vertex positions with the smallest optimization objective, the largest target PVDR, and the best OAR sparing.ConclusionsA new LATTICE treatment planning method is proposed and validated that can optimize lattice vertex positions as well as other photon or proton plan variables for improving target PVDR and OAR sparing.