A linear programming approach to inverse planning in Gamma Knife radiosurgery

PURPOSE: Leksell Gamma Knife(®) is a stereotactic radiosurgery system that allows fine‐grained control of the delivered dose distribution. We describe a new inverse planning approach that both resolves shortcomings of earlier approaches and unlocks new capabilities. METHODS: We fix the isocenter positions and perform sector‐duration optimization using linear programming, and study the effect of beam‐on time penalization on the trade‐off between beam‐on time and plan quality. We also describe two techniques that reduce the problem size and thus further reduce the solution time: dualization and representative subsampling. RESULTS: The beam‐on time penalization reduces the beam‐on time by a factor 2–3 compared with the naïve alternative. Dualization and representative subsampling each leads to optimization time‐savings by a factor 5–20. Overall, we find in a comparison with 75 clinical plans that we can always find plans with similar coverage and better selectivity and beam‐on time. In 44 of these, we can even find a plan that also has better gradient index. On a standard GammaPlan workstation, the optimization times ranged from 2.3 to 26 s with a median time of 5.7 s. CONCLUSION: We present a combination of techniques that enables sector‐duration optimization in a clinically feasible time frame.