High dose-rate (HDR) brachytherapy is a specific type of radiotherapy used to treat tumours of for example the cervix, prostate, and breasts. In HDR brachytherapy applicators are implanted into or close to the tumour volume. A radioactive source is moved through these applicators and stops at certain positions, known as dwell points. For each patient an anatomy-based dose plan is created that decides for example where to place the applicators, which dwell points to use, and for how long. The aim when creating a dose plan is to deliver an as high dose as possible to the tumour while simultaneously keeping the dose to the surrounding healthy organs as low as possible.
In order to improve the quality of dose plans mathematical optimization methods are today used in clinical practice. Usually one solves a linear penalty model that minimizes a weighted deviation from dose intervals provided by a physician. In this thesis we study certain properties and alterations of this model.
One interesting property of the model that we study is the distribution of the basic variables. We show that due to the distribution of these variables only a limited number of dwell positions can be used. Since relatively few dwell positions are used some of the corresponding dwell times have to be long in order for the desired overall dose level to be reached. These long dwell times have been observed in clinical practice and are considered to be a problem.
Another property that we study is the correlation between the objective value of the linear penalty model and dose-volume parameters used for evaluation of dose plans. We show that the correlation is weak, which implies that optimizing the linear penalty model does not give a solution to the correct problem.
Some alternative models are also considered. One that includes into the optimization the decision of where to place the applicators, when HDR brachytherapy is applied for prostate cancer, and one that reduces the long dwell times by using piecewise linear penalties. The solutions to both models show significant improvements.