Hierarchical 4πMonte Carlo-based proton beam angle pre-screening framework: a proof-of-concept

Objective. Current proton beam-angle optimization (BAO) methods are constrained by limited angular candidate sets and the high computational cost of Monte Carlo (MC)-based dose evaluation, hindering practical implementation of full-sphere (4π) optimization. We propose a 4πBAO framework that integrates beam's-eye-view (BEV) target projection filtering, water-equivalent path-length (WEPL)-based range assessment, and linear energy transfer (LET) pre-screening to reduce the angular search space prior to full MC simulation.Approach. The proposed 4πBAO framework consists of two phases: (1) a fast hierarchical pre-screening stage that uses raytracing to combine target visibility, WEPL, and analytical dose-weighted LET (dLET) evaluation, and (2) MC dose simulation applied to the reduced set of non-coplanar beams. A Geant4-based conceptual toy model with a centrally located soft-tissue target, six organ-at-risk (OAR) structures with varied material compositions arranged along orthogonal axes, and an adjacent toroidal blood OAR was used to evaluate 684 candidate beams generated by uniform full sphere angular sampling using 10° increments in polar (couch) and azimuthal (gantry) angles. A graphical user interface was implemented to visualize candidate beam angles, apply pre-screening thresholds, and transfer the filtered beam set to the MC simulation stage.Main results. From the initial 684 candidate beams, 72 met the ⩾95% target-visibility criterion following BEV-based OAR filtering. Two-tier WEPL filtering identified en-face beam paths based on target proximity and width (distal minus proximal edge), reducing the set to 52 beams and further refining it to 48 beams through analytical dLET filtering. Pre-screening was completed in <5 min. The subsequent MC simulation, implemented within a standalone in-house optimization algorithm, required 71 min. On a 64-bit, 32 GB RAM, 12-core CPU system and demonstrated feasibility of dose calculation in the conceptual phantom, achieving prescription-level target coverage with target D95% = 54 Gy, D98% = 52.9 Gy, and D2% = 62.7 Gy for Rx = 54 Gy, and toroidal OAR D50% = 40.6 Gy with Dmax = 54.2 Gy.Significance. A hierarchical 4πproton BAO framework combining pre-screening with MC-based simulation was shown to be computationally feasible while effectively leveraging non-coplanar beam configurations.