To deliver high quality intensity modulated radiotherapy (IMRT) using a novel generalized sparse orthogonal collimators (SOCs), the authors introduce a novel direct aperture optimization (DAO) approach based on discrete rectangular representation.
A total of seven patients—two glioblastoma multiforme, three head & neck (including one with three prescription doses), and two lung—were included. 20 noncoplanar beams were selected using a column generation and pricing optimization method. The SOC is a generalized conventional orthogonal collimators with N leaves in each collimator bank, where N = 1, 2, or 4. SOC degenerates to conventional jaws when N = 1. For SOC-based IMRT, rectangular aperture optimization (RAO) was performed to optimize the fluence maps using rectangular representation, producing fluence maps that can be directly converted into a set of deliverable rectangular apertures. In order to optimize the dose distribution and minimize the number of apertures used, the overall objective was formulated to incorporate an L2 penalty reflecting the difference between the prescription and the projected doses, and an L1 sparsity regularization term to encourage a low number of nonzero rectangular basis coefficients. The optimization problem was solved using the Chambolle–Pock algorithm, a first-order primal–dual algorithm. Performance of RAO was compared to conventional two-step IMRT optimization including fluence map optimization and direct stratification for multileaf collimator (MLC) segmentation (DMS) using the same number of segments. For the RAO plans, segment travel time for SOC delivery was evaluated for the N = 1, N = 2, and N = 4 SOC designs to characterize the improvement in delivery efficiency as a function of N.
Comparable PTV dose homogeneity and coverage were observed between the RAO and the DMS plans. The RAO plans were slightly superior to the DMS plans in sparing critical structures. On average, the maximum and mean critical organ doses were reduced by 1.94% and 1.44% of the prescription dose. The average number of delivery segments was 12.68 segments per beam for both the RAO and DMS plans. The N = 2 and N = 4 SOC designs were, on average, 1.56 and 1.80 times more efficient than the N = 1 SOC design to deliver. The mean aperture size produced by the RAO plans was 3.9 times larger than that of the DMS plans.
The DAO and dose domain optimization approach enabled high quality IMRT plans using a low-complexity collimator setup. The dosimetric quality is comparable or slightly superior to conventional MLC-based IMRT plans using the same number of delivery segments. The SOC IMRT delivery efficiency can be significantly improved by increasing the leaf numbers, but the number is still significantly lower than the number of leaves in a typical MLC.