Optimization in treatment planning of high dose-rate brachytherapy - Review and analysis of mathematical models

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.