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Optimization approaches to volumetric modulated arc therapy planning
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10. For clarity: By VMAT planning, we refer to treatment planning for conventional hardware, i.e. Linacs equipped with MLCs. We exclude specialized hardware such as tomotherapy.
11. An exception are dose-volume constraints, which are nonconvex. However, the nonconvexity does typically not coarse difficulties in finding high quality IMRT plans.
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14. Unless the gantry stops.
15. Unfortunately, current VMAT implementations do not always realize this potential.
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25. In this paper, we do not review FMO methods as this component does not require VMAT specific modifications. However, regularization of the FMO problem to favor smooth fluence maps is typically recommended for arc sequencing.
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30. The nonlinear relations (6) and (7) define the objective function, but are not formal constraints themselves.
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34. The gradient (12) exists everywhere if the objective function is one-time continuously differentiable in dose and zj is smooth relative to the leaf positions. The piecewise linear definition of zj according to Fig. 3 does not possess the necessary smoothness, but this issue can be resolved through the definition of a piecewise smooth gradient or the use of a more sophisticated physical fluence model.
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39. Note that, in order to communicate the VMAT plan through DICOM, the arrival/departure times have to be converted into a different piecewise linear leaf trajectory, i.e. control points.
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Volumetric modulated arc therapy (VMAT) has found widespread clinical application in recent years. A large number of treatment planning studies have evaluated the potential for VMAT for different disease sites based on the currently available commercial implementations of VMAT planning. In contrast, literature on the underlying mathematical optimization methods used in treatment planning is scarce. VMAT planning represents a challenging large scale optimization problem. In contrast to fluence map optimization in intensity-modulated radiotherapy planning for static beams, VMAT planning represents a nonconvex optimization problem. In this paper, the authors review the state-of-the-art in VMAT planning from an algorithmic perspective. Different approaches to VMAT optimization, including arc sequencing methods, extensions of direct aperture optimization, and direct optimization of leaf trajectories are reviewed. Their advantages and limitations are outlined and recommendations for improvements are discussed.
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