Graduate School of Health Sciences, Tokushima University, 3-18-15 Kuramoto, Tokushima 770-8509, Japan.
Faculty of Science, Tanta University, El-Giesh St., Tanta, Gharbia 31527, Egypt.
Comput Math Methods Med. 2020 Sep 3;2020:3096067. doi: 10.1155/2020/3096067. eCollection 2020.
We give a novel approach for obtaining an intensity-modulated radiation therapy (IMRT) optimization solution based on the idea of continuous dynamical methods. The proposed method, which is an iterative algorithm derived from the discretization of a continuous-time dynamical system, can handle not only dose-volume but also mean-dose constraints directly in IMRT treatment planning. A theoretical proof for the convergence to an equilibrium corresponding to the desired IMRT planning is given by using the Lyapunov stability theorem. By introducing the concept of "acceptable," which means the existence of a nonempty set of beam weights satisfying the given dose-volume and mean-dose constraints, and by using the proposed method for an acceptable IMRT planning, one can resolve the issue that the objective and evaluation are different in the conventional planning process. Moreover, in the case where the target planning is totally unacceptable and partly acceptable except for one group of dose constraints, we give a procedure that enables us to obtain a nearly optimal solution close to the desired solution for unacceptable planning. The performance of the proposed approach for an acceptable or unacceptable planning is confirmed through numerical experiments simulating a clinical setup.
我们提出了一种基于连续动力方法思想的获取强度调制放射治疗（IMRT）优化解的新方法。所提出的方法是从连续时间动力系统的离散化导出的迭代算法，不仅可以直接在 IMRT 治疗计划中处理剂量-体积，还可以处理平均剂量约束。通过使用 Lyapunov 稳定性定理，给出了对应于期望的 IMRT 计划的平衡状态收敛的理论证明。通过引入“可接受”的概念，这意味着存在一组非空的射束权重满足给定的剂量-体积和平均剂量约束，并且通过使用所提出的方法进行可接受的 IMRT 计划，可以解决目标和评估在传统计划过程中不同的问题。此外，在目标计划完全不可接受，除了一组剂量约束外部分可接受的情况下，我们给出了一个程序，使我们能够获得接近不可接受计划的期望解决方案的近最优解决方案。通过模拟临床设置的数值实验验证了可接受或不可接受计划的所提出方法的性能。
