Washington University School of Medicine, St. Louis, Missouri 63110, USA.
Med Phys. 2010 Aug;37(8):4056-67. doi: 10.1118/1.3453575.
The primary goal of this article is to formulate volumetric modulated arc therapy (VMAT) delivery problem and study interdependence between several parameters (beam dose rate, gantry angular speed, and MLC leaf speed) in the delivery of VMAT treatment plan. The secondary aim is to provide delivery solution and prove optimality (minimal beam on time) of the solution. An additional goal of this study is to investigate alternative delivery approaches to VMAT (like constant beam dose rate and constant gantry angular speed delivery).
The problem of the VMAT delivery is formulated as a control problem with machine constraints. The relationships between parameters of arc therapy delivery are derived under the constraint of treatment plan invariance and limitations on delivery parameters. The nonuniqueness of arc therapy delivery solutions is revealed from these relations. The most efficient delivery of arc therapy is then formulated as optimal control problem and solved by geometrical methods. A computer program is developed to find numerical solutions for deliveries of specific VMAT plan.
Explicit examples of VMAT plan deliveries are computed and illustrated with graphical representations of the variability of delivery parameters. Comparison of delivery parameters with that of Varian's delivery are shown and discussed. Alternative delivery strategies such as constant gantry angular speed delivery and constant beam dose rate delivery are formulated and solutions are provided. The treatment times for all the delivery solutions are provided.
The investigations derive and prove time optimal VMAT deliveries. The relationships between delivery parameters are determined. The optimal alternative delivery strategies are discussed.
本文的主要目的是制定容积旋转调强弧形治疗（VMAT）的剂量传递问题，并研究在 VMAT 治疗计划传递中几个参数（射束剂量率、机架旋转速度和叶片传输速度）之间的相互依赖性。次要目的是提供传递解决方案，并证明该解决方案的最优性（最小的射束开启时间）。本研究的另一个目的是研究 VMAT 的替代传递方法（如恒定射束剂量率和恒定机架旋转速度传递）。
VMAT 传递问题被表述为具有机器约束的控制问题。在治疗计划不变性和传递参数限制的约束下，导出了弧形治疗传递参数之间的关系。从这些关系中揭示了弧形治疗传递解决方案的非唯一性。然后，将最有效的弧形治疗传递表述为最优控制问题，并通过几何方法求解。开发了一个计算机程序，用于寻找特定 VMAT 计划的传递的数值解。
计算了 VMAT 计划传递的显式示例，并通过传递参数的变化的图形表示进行了说明。展示并讨论了与瓦里安（Varian）传递的传递参数的比较。还制定了恒定机架旋转速度传递和恒定射束剂量率传递等替代传递策略，并提供了解决方案。提供了所有传递解决方案的治疗时间。
研究得出并证明了时间最优的 VMAT 传递。确定了传递参数之间的关系。讨论了最优的替代传递策略。
