A Multiobjective Approach for Sector Duration Optimization in Stereotactic Radiosurgery Treatment Planning

TL;DR

This paper introduces a multiobjective linear programming approach with machine learning enhancements for optimizing sector durations in stereotactic radiosurgery, leading to better treatment plans and reduced computation time.

Contribution

It presents a novel multiobjective model and a two-phase solution strategy with machine learning to improve solution quality and efficiency in radiosurgery planning.

Findings

Solutions often outperform clinical results

Machine learning reduces computation time by nearly half

Enhanced algorithms improve solution diversity and quality

Abstract

Sector duration optimization (SDO) is a problem arising in treatment planning for stereotactic radiosurgery on Gamma Knife. Given a set of isocenter locations, SDO aims to select collimator size configurations and irradiation times thereof such that target tissues receive prescribed doses in a reasonable amount of treatment time, while healthy tissues nearby are spared. We present a multiobjective linear programming model for SDO to generate a diverse collection of solutions so that clinicians can select the most appropriate treatment. We develop a generic two-phase solution strategy based on the epsilon-constraint method for solving multiobjective optimization models, which aims to systematically increase the number of high-quality solutions obtained, instead of conducting a traditional uniform search. To improve solution quality further and to accelerate the procedure, we incorporate some general and problem-specific enhancements. Moreover, we propose an alternative version of our two-phase strategy, which makes use of machine learning tools to reduce the computational effort. In our computational study on eight previously treated real test cases, a significant portion of obtained solutions outperformed clinical results and those from a single-objective model from the literature. In addition to significant benefits of the algorithmic enhancements, our experiments illustrate the usefulness of machine learning strategies to reduce the overall run times nearly by half while maintaining or besting the clinical practice.