Purpose: Gamma Knife (GK) is a widely used stereotactic radiosurgery system for brain lesion treatment. Its treatment planning, however, may require solving a large-scale optimization to determine many variables, including an unknown number of isocenter positions, collimators, and intensities. We propose a hierarchical optimization framework to address this large-scale problem.
Methods: The framework is built by three critical components: kernel-decomposition-based (KD) dose model; multi-resolution shot initialization and dose grid with shot migration capability; and hierarchical collimator optimization. The KD dose is a shift-invariant kernel scaled by the normalized mean TMR. Both shot initialization and dose grid take resolutions of 1, 2, and 4 mm on the 1-mm-margin, 2-mm-margin, and the remaining interiors of the region of interest (ROI), respectively. For shot initialization, the ROI is the target; while for dose grid, the ROIs are the 4-mm dilations of the planning structures, including the target and organs-at-risk. Hierarchical collimator optimization starts with cones for shot locations and migrations followed by sector durations. Though not limited to, the optimization is primarily based on linear programming for its simplicity and effectiveness in sparse solution. We tested this framework using 12 AVM clinical cases retrospectively.
Results: The KD dose had Gamma Index (2%/2 mm) passing rates of 99% compared with Monte Carlo calculation for the studied cases and linear complexity that calculated shot dose in sub seconds. The sampling strategy further reduced the complexity compared to using the whole ROI without losing its representation. Hierarchical collimator optimization sped up the convergence and completed in few seconds. Compared to the clinical plans, the optimized plans by this framework on average had improved coverage (96%->100%), selectivity (62%->78%), homogeneity (1.99->1.62), gradient index (5.42->3.78), and radiation time (59min->55min).
Conclusion: The proposed framework addresses multiple fundamental aspects in GK optimization for efficient and quality treatment planning.
Funding Support, Disclosures, and Conflict of Interest: This work was supported in part by NIH grants (R01 CA235723, R01 CA218402).
Treatment Planning, Gamma Knife, Optimization