Treatment planning in high dose-rate brachytherapy has traditionally been conducted with manual forward planning, but inverse planning is today increasingly used in clinical practice. There is a large variety of proposed optimization models and algorithms to model and solve the treatment planning problem. Two major parts of inverse treatment planning for which mathematical optimization can be used are the decisions about catheter placement and dwell time distributions. Both these problems as well as integrated approaches are included in this review. The proposed models include linear penalty models, dose–volume models, mean-tail dose models, quadratic penalty models, radiobiological models, and multiobjective models. The aim of this survey is twofold: (i) to give a broad overview over mathematical optimization models used for treatment planning of brachytherapy and (ii) to provide mathematical analyses and comparisons between models. New technologies for brachytherapy treatments and methods for treatment planning are also discussed. Of particular interest for future research is a thorough comparison between optimization models and algorithms on the same dataset, and clinical validation of proposed optimization approaches with respect to patient outcome.

中文翻译：

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高剂量率近距离放射治疗的治疗方案优化—数学模型的回顾和分析

传统上，高剂量率近距离放射治疗中的治疗计划是通过人工前瞻性计划进行的，但如今反向计划已越来越多地用于临床实践中。提出了各种各样的优化模型和算法来建模和解决治疗计划问题。可以使用数学优化的逆治疗计划的两个主要部分是关于导管放置和停留时间分布的决策。这些问题以及综合方法都包含在本评价中。提议的模型包括线性惩罚模型，剂量-体积模型，平均尾部剂量模型，二次惩罚模型，放射生物学模型和多目标模型。这项调查的目的是双重的：（i）概述用于近距离放射治疗的数学优化模型，以及（ii）提供模型之间的数学分析和比较。还讨论了近距离治疗的新技术和治疗计划的方法。未来研究特别感兴趣的是，对同一数据集上的优化模型和算法进行全面比较，并针对患者的治疗结果对所提出的优化方法进行临床验证。