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

Clinical Snapshot

Key Findings

• P Value: Not reported

• Effect Size: Composite objective: 1.95 (LPO) vs 1.90 (best random) vs 2.40 (median random) vs 2.93 (worst random)

• Primary Outcome: Composite objective value improvement in lattice radiotherapy planning

• Nnt Or Sensitivity: 4-13 peaks selected from 150-400 candidate locations per case

• Confidence Interval: Not reported

Clinical Application

Requires computational infrastructure and integration with treatment planning systems; mathematical framework appears implementable Relevant to Australian radiation oncology centres using proton therapy or considering lattice techniques; aligns with TGA requirements for treatment planning software validation Patients requiring lattice radiotherapy for large tumors where peak placement optimization could improve treatment outcomes

Abstract

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.

References

1. 1.Shinde, N., Gu, W., Domal, S., Badiyan, S. N., Lin, Y., & Gao, H. (2026). Lattice peak optimization: a mixed-integer framework for geometry-adaptive lattice radiotherapy. Physics in Medicine and Biology. https://doi.org/10.1088/1361-6560/ae6d7b