A Group-Sparsity Based Optimization Framework for Automated Isocenter Selection In Gamma Knife Radiosurgery
Abstract
Purpose
Current Gamma Knife (GK) planning typically decouples isocenter placement (heuristic-based) from sector duration optimization (SDO). This separation often leads to suboptimal plan quality and prolonged beam-on time (BOT). We propose an Integrated Isocenter and Sector Duration Optimization (ISDO) framework that achieves dose-driven isocenter selection and fluence optimization simultaneously within a unified inverse-planning process.
Methods
A dense set of candidate isocenters (1-mm grid) was defined within the target volume. The ISDO objective function incorporates quadratic dose fidelity terms for targets and Organs at Risk (OARs), a Moreau-Yosida regularized BOT penalty, and a group-sparsity term for automatic isocenter selection. The optimization was solved using the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). Post-processing includes probability-driven shot sequencing and reduction to ensure deliverability. The framework was evaluated on 12 clinical cases (Arteriovenous Malformation (AVM), Vestibular Schwannoma (VS), Meningioma, Pituitary Adenoma) and compared against clinical plans.
Results
Compared to clinical plans, ISDO reduced the number of shots by 15.1% and significantly decreased BOT by 20.8% on average. Despite using fewer irradiation resources, plan quality improved: the Paddick conformity index and selectivity increased by 5.8% and 5.8%, respectively. Steepness of dose fall-off improved, with Gradient Index (GI) and Dose at 2 cm (D2cm) decreasing by 6.5% and 5.2%. OAR sparing was substantially enhanced, with mean dose reductions of 28.8% across critical structures.
Conclusion
The ISDO framework effectively unifies isocenter selection and inverse planning, producing more efficient and conformal GK plans than current heuristic-driven clinical approaches. By explicitly modeling BOT and sparsity, the system minimizes operator dependency while improving delivery efficiency and OAR sparing.