Robust Direct Aperture Optimization for Radiation Therapy Treatment Planning

Intensity-modulated radiation therapy (IMRT) allows for the design of customized, highly conformal treatments for cancer patients. Creating IMRT treatment plans, however, is a mathematically complex process, which is often tackled in multiple, simpler stages. This sequential approach typically separates radiation dose requirements from mechanical deliverability considerations, which may result in suboptimal treatment quality. For patient health to be considered paramount, holistic models must address these plan elements concurrently, eliminating quality loss between stages. This combined direct aperture optimization (DAO) approach is rarely paired with uncertainty mitigation techniques, such as robust optimization, because of the inherent complexity of both parts. This paper outlines a robust DAO (RDAO) model and discusses novel methodologies for efficiently integrating salient constraints. Because the highly complex RDAO model is difficult to solve, an original candidate plan generation (CPG) heuristic is proposed. The CPG produces rapid, high-quality, feasible plans, which are immediately clinically viable and can also be used to generate a feasible incumbent solution for warm-starting the RDAO model. Computational results obtained using clinical patient data sets with motion uncertainty show the benefit of incorporating the CPG, in terms of both the first incumbent solution and final output plan quality. Summary of Contribution: This paper describes the derivation, implementation, and solution of a large-scale robust direct aperture optimization model for the problem of intensity-modulated radiation therapy planning for cancer treatment. The contribution to operations research lies in the design of a novel mixed-integer programming model that describes all salient mechanical and clinical deliverability requirements for modern delivery equipment. Because of the large-scale nature of the resulting model, a novel tractable heuristic for generating high-quality, feasible treatment plans, as well as warm starts for the full model, is proposed and demonstrated on five clinical patient data sets.