A column generation heuristic for VMAT planning with adaptive CVaR constraints

Abstract

In this study we develop an efficient computational procedure that generates medically acceptable treatment plans for volumetric modulated arc therapy with constant gantry speed. Our proposed method is a column generation heuristic based on a mixed integer linear programming model, where the objective function contains minimization of total monitor unit of the treatment plan and dose-volume requirements are included as conditional value-at-risk constraints. Our heuristic generates a full treatment arc for the restricted master problem and calibrates the right hand side parameters of the conditional value-at-risk constraints in the first phase. In the second phase, this initial solution is improved by performing column generation. This is a fully automated procedure and produces treatment plans in a single call without any human intervention. We evaluate its performance on real prostate cancer data by comparing the quality of the generated plans with those obtained by a widely used commercial treatment planning system. Our analysis shows that the results are promising, and the generated plans satisfy the prescription restrictions and require fewer monitor units on average compared to the ones obtained using Eclipse.

A practical algorithm for VMAT optimization using column generation techniques

“…Nevertheless, several critical vacua, from the perspective of clinical practice, remain in existing CG‐based VMAT planning algorithms. First, despite the fact that a zero or close‐to‐zero dose rate can cause frequent interruptions or even termination of the beam delivery due to the machine limitation, a strictly positive lower bound (LB) for the dose rate has not been forced in existing CG‐based models 24,27,28 . Second, treatment efficiency (delivery time) is not considered in most existing CG‐based VMAT planning, such as in Peng et al 24 .…”

“…First, despite the fact that a zero or close-to-zero dose rate can cause frequent interruptions or even termination of the beam delivery due to the machine limitation, a strictly positive lower bound (LB) for the dose rate has not been forced in existing CG-based models. 24,27,28 Second, treatment efficiency (delivery time) is not considered in most existing CG-based VMAT planning, such as in Peng et al 24 Because the major advantage of VMAT compared with traditional IMRT is better efficiency, 3 a more practical VMAT strategy should explicitly incorporate delivery time in optimization and planning. To the best of our knowledge, the only CG-based VMAT planning approach that directly models the delivery time is proposed by Mahnam et al 27 Nonetheless, their approach can only control delivery time in an implicit manner via bi-criteria optimization.…”

“…The fourth DAO‐based approach for VMAT inverse planning is to iteratively generate apertures by alternating between two steps until a stopping criterion is fulfilled 23–28 . In Step 1, the algorithm optimizes the plan intensity for all given apertures.…”

“…additionally take into account treatment delivery time in their modeling. In Dursun's 28 model, dose–volume requirements expressed as conditional value‐at‐risk (CVAR) constraints were added as part of the constraints. The objective is to minimize the total MU for treatment efficiency optimization.…”

“…Three important studies of the CG-based algorithm for VMAT optimization have been performed by Peng et al, 24 Mahnam et al, 27 and Dursun et al 28 Their algorithms build upon the CG method by Men et al 25 By incorporating the restriction of dose rate and mechanical motion of the original model, the revised CG-based algorithm 24 pushes optimization modules one more step further toward practical clinical usage. Mahnam et al 27 additionally take into account treatment delivery time in their modeling.…”