A shortest-path and ADMM-based fluence-level optimization framework for discretized non-coplanar VMAT

In non-coplanar volumetric modulated arc therapy (VMAT) planning, beam trajectory selection (BTS) and fluence map optimization (FMO) are closely coupled. Within a discretized fluence-level approximation, we formulate this coupling as an integrated mixed-integer nonlinear programming (MINLP) model.

We solve the resulting MINLP using an alternating optimization strategy. For the BTS subproblem, we construct an ordered layered graph and reformulate dual-trajectory selection as a (2,δ)-partially vertex-disjoint shortest path problem, for which both exact and heuristic algorithms are developed. For the FMO subproblem, we formulate it as a continuous convex optimization problem and solve it using inexact alternating direction method of multipliers (ADMM).

We evaluate the proposed framework on four standard matRad benchmark cases (TG119 C-shape, prostate, liver, and head-and-neck) using a simplified discretized non-coplanar angular test platform. Under this experimental setting, the proposed framework suggested favorable organ-at-risk sparing trends relative to the coplanar and greedy baselines while generally maintaining comparable target coverage.

The proposed framework is intended as a fluence-level co-optimization approach for discretized non-coplanar VMAT planning, rather than as a complete clinical VMAT delivery optimization system. The results indicate that explicit coupling of BTS and FMO is feasible under the adopted discretized angular setting. These findings provide a methodological basis for future incorporation of direct aperture optimization and dynamic multileaf collimator trajectory modeling.