Brachytherapy is a treatment method for various forms of cancers which involves delivering radiation directly into, or near, the tumor by passing radioactive material through catheters that are placed in the patient’s body. Optimization models are commonly used while planning high dose-rate brachytherapy treatments of prostate cancers. In particular models based on linear or quadratic penalties have been shown to produce clinically viable plans. During treatment planning there are several sources of uncertainty. Imaging techniques using ultrasound produces fuzzy boundaries, medical equipments have certain levels of permitted inaccuracies, etc. These factors can lead to discrepancies between the model and the real world. The models used does not take these types of uncertainties into account which could pose a risk of insufficient treatment in practice. This thesis investigates an approach for iteratively increasing a linear penalty model’s resistance to inherently small errors and uncertainties in the data used. The aim of this approach is to mitigate potential issues in treatment quality stemming from uncertainties. The proposed algorithm consists of iteratively adding constraints to the linear penalty model which represents different cases of realized uncertainties. These constraints are generated based on the solutions of a MIP model which, given a plan, introduces errors to the catheter placements such that the penalty is maximized. The ultimate goal is to find the worst possible case so that the model can take that into account when generating a treatment plan. The primary finding is that the robustness increases while applying this proposed algorithm. The quality of the plans generated has a similar quality to the non-robust plans. However the computational costs must be greatly reduced before this algorithm can see any practical use.
Christoffer Holm (2026) studied this question.