A linear implementation of dose-volume constraints for multi-criteria optimization

Dose-volume constraints are widely used in inverse planning for radiation therapy. Given the intricate combinatorial nature of the problem, existing approaches suffer from long runtimes, insufficient approximation of the constraints, or the necessity to specify reasonable starting values a priori. This can be problematic, particularly when planning is considered as a multi-criteria optimization problem. We present a new method to handle dose-volume constraints during planning for robotic radiosurgery. Taking into account the typically very conformal nature of the resulting dose distributions, we specify the constraints on a small subset of points instead of the full volume. We show how this allows for an effective relaxation of the problem. Results for a prostate case indicate that the proposed method leads to good approximations of the dose-volume constraints and is independent of the optimization objective.