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A shortest-path and ADMM-based fluence-level optimization framework for discretized non-coplanar VMAT
Fengjuan Wang1, Yiming Wang1, Feifan Nong1
1Institute of Operations Research and Information Engineering, Beijing University of Technology, Beijing, 100124, China.
Computer Methods and Programs in Biomedicine
|June 17, 2026
Summary
This study presents a new method for non-coplanar volumetric modulated arc therapy (VMAT) planning, integrating beam trajectory selection (BTS) and fluence map optimization (FMO). The approach shows improved organ-at-risk sparing in VMAT planning.
Area of Science:
- Medical Physics
- Radiation Oncology
- Computational Optimization
Background:
- Beam trajectory selection (BTS) and fluence map optimization (FMO) are interdependent in non-coplanar volumetric modulated arc therapy (VMAT) planning.
- Existing methods often treat BTS and FMO separately, potentially limiting treatment plan quality.
- A unified approach is needed to optimize these coupled parameters for improved VMAT delivery.
Purpose of the Study:
- To develop and evaluate an integrated mixed-integer nonlinear programming (MINLP) model for discretized non-coplanar VMAT planning.
- To couple beam trajectory selection (BTS) and fluence map optimization (FMO) within a single optimization framework.
- To assess the performance of the proposed co-optimization approach against existing methods.
Main Methods:
- Formulated a mixed-integer nonlinear programming (MINLP) model for coupled BTS and FMO in discretized non-coplanar VMAT.
- Employed an alternating optimization strategy: BTS solved via a shortest path problem on an ordered layered graph, and FMO via inexact alternating direction method of multipliers (ADMM).
- Evaluated the framework on standard matRad benchmark cases (TG119 C-shape, prostate, liver, head-and-neck).
Main Results:
- The proposed framework demonstrated favorable organ-at-risk sparing trends compared to coplanar and greedy approaches.
- Target coverage was generally maintained at a comparable level to baseline methods.
- The co-optimization approach proved feasible for discretized non-coplanar VMAT planning.
Conclusions:
- The fluence-level co-optimization of BTS and FMO is a viable strategy for discretized non-coplanar VMAT.
- This integrated framework provides a methodological foundation for future advancements, including direct aperture optimization and dynamic MLC modeling.
- The study highlights the benefits of explicitly coupling BTS and FMO for potentially enhanced radiation therapy planning.
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