Automatic Treatment Planning for Multi-focal Dynamic Conformal Arc GRID Therapy for Late Stage Lung Cancer: A Feasibility Study

Purpose: To develop a heuristic greedy algorithm to generate automatic multi-leaf collimator (MLC) sequencing for spatial fractioned radiation therapy (SFRT) using 3D dynamic conformal arc (DCA).Methods and materials: One late stage lung cancer patient with simulated sphere target grid was included in this study. N_t spheres were equally spaced within the gross target volume (GTV). The sphere targets are 1.5 cm in diameter, 4.3 cm spacing for 6,9,10, and 12 targets scenarios, and 2.8cm spacing for one special 10 targets scenario. Optimization was designed to complete within one coplanar arc from 180° to 0° in a clockwise direction with 2° as the angle interval. The problem is formalized as finding optimal MLC sequencing to cover N_t targets with K control points (CPs) for each arc. The state of each target’s MLC opening at each CP is binary. The original NP-hard problem can be approximated to a feasible subproblem by the greedy approximation on each control point and using the heuristic approach for the initial point. The algorithm focuses on the normalized relative dose relationship as the object function during the optimization. The dose matrix for each step was rasterized and grouped based on Monte Carlo simulation as the pre-calculation process. The physical speed limitation of the MLC motion was considered in the optimization to achieve a realistic and deliverable final MLC sequencing solution. Four grid arrays (6, 9, 10, and 12 targets respectively) were tested for plan quality. The arc collimator angle was planned with both 0 and 30 degrees for comparison. Prescription was set to 20 Gy to one fraction. The delivered dose will be normalized to equalize the minimum target dose to the prescription dose. Key dosimetric endpoints including target mean dose, D5, and D95, were reported. Results: The complexity of this algorithm has been reduced by a factor of \frac{2^K}{2\left(K-1\right)}. The D95 deviations of all targets as the main focus object were within 2.88% in four grid arrays with 0°/30° collimator rotation angles, 4.3 cm spacing for 6,9,10 and 12 targets scenarios, and 2.8 cm spacing for one special 10 targets scenario. For all scenarios with 4.3 cm spacing, the mean valley-to-peak ratios were under 0.45 and were within the constraint that the dose of the other part of the tumor is no more than 45% of the max normalized D95 delivered target dose during the algorithm optimization. Conclusion: This algorithm is a feasible and practical method with high efficiency while delivering the prescription dose to small target volume for late stage cancer palliative management. The proposed solution provides decent coverage to the tumor volume as well as the valley-to-peak ratio. It provides a competitive alternative solution to the standard alloy grid delivery technique.