Composite geometric modeling for directional brachytherapy: a novel approach for capsule placement optimization

This study presents a novel geometric modeling approach for directional brachytherapy, focusing on optimizing capsule placement within anatomically complex target regions. The proposed method introduces composite capsule representations, combining cylindrical bodies with spherical radiation zones, and employs normalized phi-functions to enforce spatial and angular constraints. A hybrid optimization strategy is developed, integrating online and offline packing techniques to construct and refine feasible configurations incrementally. The mathematical formulation treats the placement problem as an identical item packing problem (IIPP), incorporating nonlinear programming to manage capsule interactions and orientation control. Computational experiments were conducted across four examples with varying capsule counts, geometric parameters, and constraint settings. Results demonstrate the method’s adaptability to different anatomical conditions and effectiveness in non-parallel alignment. The approach supports anatomically conformal treatment planning.