Impact of using linear optimization models in dose planning for HDR brachytherapy

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.