Integrated isocenter and sector duration optimization (ISDO) for gamma knife radiosurgery

Current Gamma Knife (GK) treatment planning algorithms typically determine isocenter locations using geometric heuristics rather than dose-driven optimization. Isocenters are either placed automatically (using center-of-mass, skeleton-based, or curvature-based algorithms) or manually by planners, followed by a separate sector duration optimization (SDO) with fixed isocenter locations. Since the isocenter selection is separate from the dosimetry optimization, the SDO step is often constrained by a suboptimal isocenter configuration, limiting achievable plan quality and leading to unnecessarily long beam-on time (BOT). Approach. We introduce an integrated isocenter and sector duration optimization framework (ISDO) that replaces heuristic isocenter placement with a dose-driven joint isocenter and sector duration optimization. The framework includes an L_{2,1/2\ } group-sparsity model for isocenter selection and an explicit BOT regularization for delivery efficiency. The selected isocenters are further refined through an SDO module, followed by a post-processing stage that converts the optimized sector-collimator patterns into deliverable shot configuration. The framework was evaluated using 12 GK cases spanning a variety of clinical indications, including arteriovenous malformation, vestibular schwannoma, meningioma, and pituitary adenoma. Main results. With similar or better plan quality, ISDO plans used fewer or equal shots and substantially reduced the BOT. Across all cases, ISDO reduced the number of shots by 15.06% and BOT by 20.77%. With similar target coverage, the selectivity and Paddick conformity index increased by 5.77% and 5.82%, and R50 and D2cm decreased by 6.45% and 5.23%. The maximum and mean doses of organs-at-risk (OARs) were also reduced by 16.0% and 28.8% respectively. Significance. By incorporating isocenter selection directly into the BOT-aware inverse-planning framework and driving the isocenter selection through an L_{2,1/2\ } group sparsity term, the proposed ISDO method achieved more efficient and conformal GK plans than current clinical GK treatment planning approaches. .