Solving the volumetric modulated arc therapy (VMAT) problem using a sequential convex programming method

Abstract

The volumetric modulated arc therapy (VMAT) problem is highly non-convex and much more difficult than the fixed-field intensity modulated radiotherapy optimization problem. To solve it efficiently, we propose a sequential convex programming algorithm that solves a sequence of convex optimization problems. Beginning by optimizing the aperture weights of many (72) evenly distributed beams using the beam’s eye view of the target from each direction as the initial aperture shape, the search space is constrained to allowing the leaves to move within a pre-defined step-size. A convex approximation problem is introduced and solved to optimize the leaf positions and the aperture weights within the search space. The algorithm is equipped with both local and global search strategies, whereby a global search is followed by a local search: a large step-size results in a global search with a less accurate convex approximation, followed by a small step-size local search with an accurate convex approximation. The performance of the proposed algorithm is tested on three patients with three different disease sites (paraspinal, prostate and oligometastasis). The algorithm generates VMAT plans comparable to the ideal 72-beam fluence map optimized plans (i.e. IMRT plans before leaf sequencing) in 14 iterations and 36 mins on average. The algorithm is also tested on a small down-sampled prostate case for which we could computationally afford to obtain the ground-truth by solving the non-convex mixed-integer optimization problem exactly. This general algorithm is able to produce results essentially equivalent to the ground-truth but 12 times faster. The algorithm is also scalable and can handle real clinical cases, whereas the ground-truth solution using mixed-integer optimization can only be obtained for highly down-sampled cases.

Automated VMAT treatment planning using sequential convex programming: algorithm development and clinical implementation

“…Expanding this work to VMAT has been technically very challenging due mainly to the non-convexity and the growing size of the resultant optimization problems. In this work, we proposed an automated VMAT algorithm based on SCP (Dursun et al 2021) and constrained hierarchical optimization. We proposed novel convex surrogate metrics for incorporating plan complexity and promoting aperture regularity and neighboring aperture similarity.…”

Dosimetric comparison of fixed field dynamic IMRT and VMAT techniques in simultaneous integrated boost radiotherapy of prostate cancer

“…The dose constraint and optimization parameters of the three plans were the same ones, and the dose calculation grid size was 2.5 mm, using the AAA dose algorithm. [ 12 ]…”

“…Palma et al reported that the most favorable equivalent uniform doses and lowest doses to organs at risk were achieved with variable dose-rate VMAT, which was statistically significantly better than 5-field, IMRT for rectal and femoral head endpoints and better than constant dose-rate VMAT for most bladder and rectal endpoints. [11][12][13] Multiple groups have observed that VMAT reduces beam-on time and the radiation dose relative to 7 to 9 field IMRT.…”

Deep Learning 3D Dose Prediction for Conventional Lung IMRT Using Consistent/Unbiased Automated Plans

“…In this work, we employ our in-house automated treatment planning system, internally referred to expedited constrained hierarchical optimization (ECHO), to generate consistent high-quality plans as an input for our DL model. ECHO generates consistent high-quality plans by solving a sequence of constrained large-scale optimization problem [28,29,30,31,32,33]. ECHO is integrated with Eclipse and is used in our daily clinical routine, with more than 4000 patients treated to date.…”