The effect of different control point sampling sequences on convergence of VMAT inverse planning

A key component of some volumetric-modulated arc therapy (VMAT) optimization algorithms is the progressive addition of control points to the optimization. This idea was introduced in Otto's seminal VMAT paper, in which a coarse sampling of control points was used at the beginning of the optimization and new control points were progressively added one at a time. A different form of the methodology is also present in the RapidArc optimizer, which adds new control points in groups called 'multiresolution levels', each doubling the number of control points in the optimization. This progressive sampling accelerates convergence, improving the results obtained, and has similarities with the ordered subset algorithm used to accelerate iterative image reconstruction. In this work we have used a VMAT optimizer developed in-house to study the performance of optimization algorithms which use different control point sampling sequences, most of which fall into three different classes: doubling sequences, which add new control points in groups such that the number of control points in the optimization is (roughly) doubled; Otto-like progressive sampling which adds one control point at a time, and equi-length sequences which contain several multiresolution levels each with the same number of control points. Results are presented in this study for two clinical geometries, prostate and head-and-neck treatments. A dependence of the quality of the final solution on the number of starting control points has been observed, in agreement with previous works. We have found that some sequences, especially E20 and E30 (equi-length sequences with 20 and 30 multiresolution levels, respectively), generate better results than a 5 multiresolution level RapidArc-like sequence. The final value of the cost function is reduced up to 20%, such reductions leading to small improvements in dosimetric parameters characterizing the treatments-slightly more homogeneous target doses and better sparing of the organs at risk.