A practical algorithm for VMAT optimization using column generation techniques

Purpose As a challenging but important optimization problem, the inverse planning for volumetric modulated arc therapy (VMAT) has attracted much research attention. The column generation (CG) type method is so far one of the most effective solution schemes. However, it often relies on simplifications leading to significant gaps between the output and the actual feasible plan. This paper presents a novel column generation (NCG) approach to push the planning results substantially closer to practice. Methods The proposed NCG algorithm is equipped with multiple new quality-enhancing and computation-facilitating modules as below: (1) Flexible constraints are enabled on both dose rates and treatment time to adapt to machine capabilities as well as planner's preferences, respectively; (2) a cross-control-point intermediate aperture simulation is incorporated to better conform to the underlying physics; (3) new pricing and pruning subroutines are adopted to achieve better optimization outputs. To evaluate the effectiveness of this NCG, five VMAT plans, that is, three prostate cases and two head-and-neck cases, were computed using proposed NCG. The planning results were compared with those yielded by a historical benchmark planning scheme. Results The NCG generated plans of significantly better quality than the benchmark planning algorithm. For prostate cases, NCG plans satisfied all planning target volume (PTV) criteria whereas CG plans failed on D10% criteria of PTVs for over 9 Gy or more on all cases. For head-and-neck cases, again, NCG plans satisfied all PTVs criteria while CG plans failed on D10% criteria of PTVs for over 3 Gy or more on all cases as well as the max dose criteria of both cord and brain stem for over 13 Gy on one case. Moreover, the pruning scheme was found to be effective in enhancing the optimization quality. Conclusions The proposed NCG inherits the computational advantages of the traditional CG, while capturing a more realistic characterization of the machine capability and underlying physics. The output solutions of the NCG are substantially closer to practical implementation.