Lattice peak optimization: a mixed-integer framework for geometry-adaptive lattice radiotherapy

Objective.Lattice radiotherapy (LATTICE) delivers spatially distributed high-dose peaks within the tumor volume while maintaining lower doses in surrounding valley regions. Determining feasible peak locations is typically performed using heuristic or manual approaches, which may limit the number and spatial distribution of deliverable peaks. This work introduces a lattice peak optimization (LPO) framework that jointly optimizes peak placement and dose distribution to identify the maximum number of geometrically feasible peaks within the target.Approach.Proton LATTICE planning is formulated as a mixed-integer optimization problem that selects an optimal subset of peaks from a large set of candidate locations within the target. Binary variables represent peak selection and continuous variables model spot weights. The formulation enforces geometric feasibility between peaks while optimizing dosimetric objectives to improve peak-to-valley dose ratio (PVDR) and reduce organs-at-risk (OAR) dose. The resulting nonconvex problem is solved using iterative convex relaxation within an alternating direction method of multipliers framework.Main results.LPO was evaluated on three clinical cases with 150-400 candidate peak locations, from which 4-13 peaks were selected. Compared with 50-90 randomly generated LATTICE configurations per case, LPO consistently achieved higher PVDR and improved OAR sparing. In an abdominal case, the composite objective value was 2.93 (worst random), 2.40 (median random), 1.90 (best random), and 1.95 (LPO), with similar trends observed across all cases.Significance.A geometry-adaptive, mixed-integer optimization framework for lattice peak placement is presented, demonstrating improved PVDR and OAR sparing relative to manual and random LATTICE approaches. The present study evaluates performance of the proposed framework in the context of proton LATTICE planning; however, the framework is mathematically modality-agnostic and could in principle be applied to other radiation modalities.