Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02114, USA.
Phys Med Biol. 2013 Sep 7;58(17):5931-44. doi: 10.1088/0031-9155/58/17/5931. Epub 2013 Aug 6.
Stereotactic body radiation therapy (SBRT) is characterized by delivering a high amount of dose in a short period of time. In SBRT the dose is delivered using open fields (e.g., beam's-eye-view) known as 'apertures'. Mathematical methods can be used for optimizing treatment planning for delivery of sufficient dose to the cancerous cells while keeping the dose to surrounding organs at risk (OARs) minimal. Two important elements of a treatment plan are quality and delivery time. Quality of a plan is measured based on the target coverage and dose to OARs. Delivery time heavily depends on the number of beams used in the plan as the setup times for different beam directions constitute a large portion of the delivery time. Therefore the ideal plan, in which all potential beams can be used, will be associated with a long impractical delivery time. We use the dose to OARs in the ideal plan to find the plan with the minimum number of beams which is guaranteed to be epsilon-optimal (i.e., a predetermined maximum deviation from the ideal plan is guaranteed). Since the treatment plan optimization is inherently a multi-criteria-optimization problem, the planner can navigate the ideal dose distribution Pareto surface and select a plan of desired target coverage versus OARs sparing, and then use the proposed technique to reduce the number of beams while guaranteeing epsilon-optimality. We use mixed integer programming (MIP) for optimization. To reduce the computation time for the resultant MIP, we use two heuristics: a beam elimination scheme and a family of heuristic cuts, known as 'neighbor cuts', based on the concept of 'adjacent beams'. We show the effectiveness of the proposed technique on two clinical cases, a liver and a lung case. Based on our technique we propose an algorithm for fast generation of epsilon-optimal plans.
立体定向体部放射治疗（SBRT）的特点是在短时间内给予大剂量照射。在 SBRT 中，剂量是通过使用称为“孔径”的开放野（例如，视线野）来传递的。数学方法可用于优化治疗计划，以在将剂量递送至癌细胞的同时，将剂量保持在周围风险器官（OARs）的最小限度。治疗计划的两个重要要素是质量和传递时间。计划的质量基于目标覆盖率和 OARs 的剂量来衡量。传递时间在很大程度上取决于计划中使用的光束数量，因为不同光束方向的设置时间构成了传递时间的很大一部分。因此，所有潜在光束都可以使用的理想计划将与不切实际的长传递时间相关联。我们使用理想计划中的 OARs 剂量来找到具有最小光束数的计划，该计划保证是ε最优的（即，保证与理想计划的预定最大偏差）。由于治疗计划优化本质上是一个多标准优化问题，因此规划者可以在理想剂量分布 Pareto 表面上进行导航，并选择具有所需目标覆盖率和 OARs 节约的计划，然后使用所提出的技术来减少光束数量，同时保证ε最优性。我们使用混合整数规划（MIP）进行优化。为了减少由此产生的 MIP 的计算时间，我们使用了两种启发式方法：一种是光束消除方案，另一种是基于“相邻光束”概念的一系列启发式切割，称为“邻域切割”。我们在两个临床病例（肝脏和肺部病例）上展示了该技术的有效性。基于我们的技术，我们提出了一种快速生成ε最优计划的算法。
