Image Processing Center, Beihang University, Beijing 100191, People's Republic of China. Department of Radiation Oncology, National Cancer Center/Cancer Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College, Beijing 100021, People's Republic of China.
Phys Med Biol. 2018 Jan 5;63(1):015034. doi: 10.1088/1361-6560/aa9b47.
With robot-controlled linac positioning, robotic radiotherapy systems such as CyberKnife significantly increase freedom of radiation beam placement, but also impose more challenges on treatment plan optimization. The resampling mechanism in the vendor-supplied treatment planning system (MultiPlan) cannot fully explore the increased beam direction search space. Besides, a sparse treatment plan (using fewer beams) is desired to improve treatment efficiency. This study proposes a singular value decomposition linear programming (SVDLP) optimization technique for circular collimator based robotic radiotherapy. The SVDLP approach initializes the input beams by simulating the process of covering the entire target volume with equivalent beam tapers. The requirements on dosimetry distribution are modeled as hard and soft constraints, and the sparsity of the treatment plan is achieved by compressive sensing. The proposed linear programming (LP) model optimizes beam weights by minimizing the deviation of soft constraints subject to hard constraints, with a constraint on the l norm of the beam weight. A singular value decomposition (SVD) based acceleration technique was developed for the LP model. Based on the degeneracy of the influence matrix, the model is first compressed into lower dimension for optimization, and then back-projected to reconstruct the beam weight. After beam weight optimization, the number of beams is reduced by removing the beams with low weight, and optimizing the weights of the remaining beams using the same model. This beam reduction technique is further validated by a mixed integer programming (MIP) model. The SVDLP approach was tested on a lung case. The results demonstrate that the SVD acceleration technique speeds up the optimization by a factor of 4.8. Furthermore, the beam reduction achieves a similar plan quality to the globally optimal plan obtained by the MIP model, but is one to two orders of magnitude faster. Furthermore, the SVDLP approach is tested and compared with MultiPlan on three clinical cases of varying complexities. In general, the plans generated by the SVDLP achieve steeper dose gradient, better conformity and less damage to normal tissues. In conclusion, the SVDLP approach effectively improves the quality of treatment plan due to the use of the complete beam search space. This challenging optimization problem with the complete beam search space is effectively handled by the proposed SVD acceleration.
利用机器人控制的直线加速器定位，机器人放射治疗系统（如 CyberKnife）显著增加了射束放置的自由度，但也对治疗计划优化提出了更多挑战。供应商提供的治疗计划系统（MultiPlan）中的重采样机制不能充分探索增加的射束方向搜索空间。此外，希望使用较少的射束来制定稀疏的治疗计划，以提高治疗效率。本研究提出了一种基于奇异值分解线性规划（SVDLP）的机器人放射治疗圆形准直器优化技术。SVDLP 方法通过模拟用等效射束锥覆盖整个靶区的过程来初始化输入射束。将剂量分布要求建模为硬约束和软约束，并通过压缩感知实现治疗计划的稀疏性。所提出的线性规划（LP）模型通过最小化软约束对硬约束的偏差来优化射束权重，并对射束权重的 l 范数施加约束。针对 LP 模型开发了一种基于奇异值分解（SVD）的加速技术。基于影响矩阵的退化性，首先将模型压缩到较低维度进行优化，然后反向投影重建射束权重。在进行射束权重优化后，通过去除低权重射束并使用相同模型优化剩余射束的权重来减少射束数量。这种减少射束的技术通过混合整数规划（MIP）模型进一步验证。SVDLP 方法在一个肺部病例上进行了测试。结果表明，SVD 加速技术可将优化速度提高 4.8 倍。此外，与通过 MIP 模型获得的全局最优计划相比，减少射束的技术可以实现相似的计划质量，但速度要快一个到两个数量级。此外，还对 SVDLP 方法进行了测试，并与 MultiPlan 对三个具有不同复杂度的临床病例进行了比较。总体而言，SVDLP 方法生成的计划具有更陡峭的剂量梯度、更好的一致性和对正常组织的更小损伤。总之，由于使用了完整的射束搜索空间，SVDLP 方法有效地提高了治疗计划的质量。该方法通过使用完整的射束搜索空间，有效地处理了具有挑战性的优化问题。
