Lattice Peak Optimization: A Mixed-Integer Framework for Geometry-Adaptive Lattice Radiation Therapy Planning
Abstract
Purpose
Lattice radiotherapy (LATTICE) is a spatially fractionated technique that delivers high doses to discrete peak regions within the target while maintaining lower doses in surrounding valley regions, yielding a high peak-to-valley dose ratio (PVDR). Conventional LATTICE planning relies on manually or heuristically placed peaks that satisfy geometric constraints such as minimum center-to-center distance and separation from organs-at-risk (OAR). These approaches limit the number of deliverable peaks and may compromise target coverage or OAR sparing. This work introduces a lattice peak optimization (LPO) method that jointly optimizes peak placement and dose distributions to improve LATTICE plan quality while delivering the maximum number of feasible peaks within the target.
Methods
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 PVDR and reduce OAR dose. The resulting nonconvex problem is solved using iterative convex relaxation within an alternating direction method of multipliers framework.
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.
Conclusion
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 method is modality-independent and readily extendable to photon-based LATTICE planning.