Mixed integer programming improves comprehensibility and plan quality in inverse optimization of prostate HDR-brachytherapy

TL;DR

This paper introduces mixed integer programming techniques to improve the efficiency and interpretability of inverse optimization in prostate HDR brachytherapy, leading to faster solutions and better treatment plans.

Contribution

It develops new mixed integer programming models and an iterative approach that enhance plan quality and reduce computation time in prostate HDR brachytherapy planning.

Findings

Mixed integer programming reduces solution times by up to 75%.

The new dose-volume model achieves better DVH statistics.

Early stopping of solvers maintains plan quality while saving time.

Abstract

Current inverse treatment planning methods that optimize both catheter positions and dwell times in prostate HDR brachytherapy use surrogate linear or quadratic objective functions that have no direct interpretation in terms of dose-volume histogram (DVH) criteria, do not result in an optimum or have long solution times. We decrease the solution time of existing linear and quadratic dose-based programming models (LP and QP, respectively) to allow optimizing over potential catheter positions using mixed integer programming. An additional average speed-up of 75% can be obtained by stopping the solver at an early stage, without deterioration of the plan quality. For a fixed catheter configuration, the dwell time optimization model LP solves to optimality in less than 15 seconds, which confirms earlier results. We propose an iterative procedure for QP that allows to prescribe the target dose as an interval, while retaining independence between the solution time and the number of dose calculation points. This iterative procedure is comparable in speed to the LP model, and produces better plans than the non-iterative QP. We formulate a new dose-volume based model that maximizes $V_{100\%}$ while satisfying pre-set DVH-criteria. This model optimizes both catheter positions and dwell times within a few minutes depending on prostate volume and number of catheters, optimizes dwell times within 35 seconds, and gives better DVH statistics than dose-based models. The solutions suggest that the correlation between objective value and clinical plan quality is weak in existing dose-based models.