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

Area of Science:

• Medical Physics
• Radiation Oncology
• Computational Optimization

Background:

• Lattice radiotherapy (LATTICE) uses spatially distributed high-dose peaks for targeted tumor treatment.
• Current methods for determining LATTICE peak locations are often heuristic or manual, potentially limiting treatment efficacy.
• Optimizing peak placement and dose distribution simultaneously is crucial for maximizing therapeutic benefit.

Purpose of the Study:

• To introduce a novel lattice peak optimization (LPO) framework for radiotherapy.
• To jointly optimize peak placement and dose distribution for maximum geometrically feasible peaks.
• To improve the peak-to-valley dose ratio (PVDR) and reduce dose to organs at risk (OAR).

Main Methods:

• Proton LATTICE planning formulated as a mixed-integer optimization problem.
• Selection of optimal peaks from candidate locations using binary and continuous variables.
• Iterative convex relaxation within an alternating direction method of multipliers framework to solve the non-convex problem.

Main Results:

• LPO framework successfully selected 4-13 peaks from 150-400 candidates across three clinical cases.
• LPO consistently achieved higher PVDR and better OAR sparing compared to random LATTICE configurations.
• In an abdominal case, LPO yielded a composite objective value of 1.95, outperforming the best random configuration (1.90).

Conclusions:

• The proposed geometry-adaptive LPO framework enhances LATTICE planning by optimizing peak placement and dose distribution.
• LPO demonstrates superior PVDR and OAR sparing compared to existing manual and random approaches.
• The framework is modality-agnostic and applicable to various radiation modalities beyond proton therapy.