Algorithms are an essential part of radiation therapy planning, which includes three optimizations problems: beam angle configuration, fluence map, and realization. This study addresses the third one, also called the leaf sequencing problem, which arises for each chosen irradiation angle, given the optimized fluence map. It consists in defining a sequence of configurations of a device (called multileaf collimator) that correctly delivers radiation to the patient. A usual model for this problem is the decomposition of a matrix into a weighted sum of (0,1)-matrices, called segments, in which the ones in each row appear consecutively. Each (0,1)-matrix corresponds to a configuration of the device. The realization problem has three objectives. The first one is to minimize the sum of weights assigned to the (0,1)-matrices. The second is to minimize the number of segments. Finally, the third one is to find the best order to apply those configurations. This study presents a greedy and randomized algorithm to this problem and compares it with other algorithms presented previously in the literature. Statistical tests show that our algorithm outperformed the previous ones regarding the quality indicators investigated.

a Illustrates how the IMRT realization is modelled to a mathematical problem. b Shows a decomposition example of the IMRT realization. c The scheme of the algorithm that is proposed on this work, called GRA-SRA.

算法是放射治疗计划的重要组成部分，其中包括三个优化问题：束角配置，注量图和实现。这项研究解决了第三个问题，也称为叶片排序问题，在给定了最佳通量图的情况下，每个选择的照射角度都会出现该问题。它包括定义将放射线正确传送给患者的设备（称为多叶准直仪）的配置顺序。解决此问题的常用模型是将矩阵分解为（0,1）矩阵的加权总和，称为分段，其中每行中的矩阵连续出现。每个（0,1）矩阵都对应于设备的配置。实现问题具有三个目标。第一个是最小化分配给（0,1）矩阵的权重之和。第二是尽量减少段数。最后，第三个是找到应用这些配置的最佳顺序。本研究针对此问题提出了一种贪婪的随机算法，并将其与文献中先前提出的其他算法进行了比较。统计测试表明，在所研究的质量指标方面，我们的算法优于以前的算法。

a说明如何将IMRT实现建模为数学问题。b显示了IMRT实现的分解示例。c这项工作中提出的算法方案，称为GRA-SRA。