Department of Mathematics, Linköping University, SE 581 83 Linköping, Sweden.
Med Phys. 2012 Feb;39(2):1021-8. doi: 10.1118/1.3676179.
Dose plans generated with optimization models hitherto used in high-dose-rate (HDR) brachytherapy have shown a tendency to yield longer dwell times than manually optimized plans. Concern has been raised for the corresponding undesired hot spots, and various methods to mitigate these have been developed. The hypotheses upon this work is based are (a) that one cause for the long dwell times is the use of objective functions comprising simple linear penalties and (b) that alternative penalties, as these are piecewise linear, would lead to reduced length of individual dwell times.
The characteristics of the linear penalties and the piecewise linear penalties are analyzed mathematically. Experimental comparisons between the two types of penalties are carried out retrospectively for a set of prostate cancer patients.
When the two types of penalties are compared, significant changes can be seen in the dwell times, while most dose-volume parameters do not differ significantly. On average, total dwell times were reduced by 4.2%, with a reduction of maximum dwell times by 25%, when the alternative penalties were used.
The use of linear penalties in optimization models for HDR brachytherapy is one cause for the undesired long dwell times that arise in mathematically optimized plans. By introducing alternative penalties, a significant reduction in dwell times can be achieved for HDR brachytherapy dose plans. Although various measures for mitigating the long dwell times are already available, the observation that linear penalties contribute to their appearance is of fundamental interest.
迄今用于高剂量率（HDR）近距离放射治疗的优化模型生成的剂量计划显示出比手动优化计划更长的驻留时间的趋势。人们对相应的不理想热点表示担忧，并开发了各种减轻这些热点的方法。这项工作的假设基于（a）驻留时间长的一个原因是使用包含简单线性惩罚的目标函数，以及（b）替代惩罚（因为它们是分段线性的）会导致单个驻留时间的长度减少。
从数学上分析了线性惩罚和分段线性惩罚的特征。对一组前列腺癌患者进行了回顾性实验比较，比较了这两种类型的惩罚。
当比较这两种类型的惩罚时，可以看到驻留时间有显著变化，而大多数剂量-体积参数没有显著差异。当使用替代惩罚时，平均总驻留时间减少了 4.2%，最大驻留时间减少了 25%。
在 HDR 近距离放射治疗的优化模型中使用线性惩罚是导致数学优化计划中出现不必要的长驻留时间的原因之一。通过引入替代惩罚，可以显著减少 HDR 近距离放射治疗剂量计划的驻留时间。尽管已经有各种减轻长驻留时间的措施，但观察到线性惩罚会导致它们出现，这具有根本的意义。
