A mathematical optimization model for spatial adjustments of dose distributions in high dose-rate brachytherapy

High dose-rate brachytherapy is a modality of radiation therapy used for cancer treatment, in which the radiation source is placed within the body. The treatment goal is to give a high enough dose to the tumour while sparing nearby healthy tissue and organs (organs-at-risk). The most common criteria for evaluating dose distributions are dosimetric indices. For the tumour, such an index is the portion of the volume that receives at least a specified dose level (e.g. the prescription dose), while for organs-at-risk it is instead the portion of the volume that receives at most a specified dose level. Dosimetric indices are aggregate criteria and do not consider spatial properties of the dose distribution. Further, there are neither any established evaluation criteria for characterizing spatial properties, nor have such properties been studied in the context of mathematical optimization of brachytherapy. Spatial properties are however of clinical relevance and therefore dose plans are sometimes adjusted manually to improve them. We propose an optimization model for reducing the prevalence of contiguous volumes with a too high dose (hot spots) or a too low dose (cold spots) in a tentative dose plan. This model is independent of the process of constructing the tentative plan. We conduct computational experiments with tentative plans obtained both from optimization models and from clinical practice. The objective function considers pairs of dose points and each pair is given a distance-based penalty if the dose is either too high or too low at both dose points. Constraints are included to retain dosimetric indices at acceptable levels. Our model is designed to automate the manual adjustment step in the planning process. In the automatic adjustment step large-scale optimization models are solved. We show reductions of the volumes of the largest hot and cold spots, and the computing times are feasible in clinical practice.