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Intensity-modulated radiation therapy (IMRT) is a commonly-used method for treating cancer. To develop a treatment plan, an optimization problem is formulated to find the optimal radiation intensities to ensure that the cancerous region receives the required prescribed radiation dose while limiting the excess radiation to the surrounding healthy organs. Due to the granularity of the discretization of the body into numerous three-dimensional pixels, the resulting optimization problem is often extremely large-scale and can include tens of thousands of constraints. This paper presents an exact dose-based constraint generation technique to solve large-scale linear problems in IMRT. We first use specific characteristics of the IMRT problem to cluster the voxels based on how they are influenced per unit intensity of each part of the radiation beams and then use these clusters in a specialized constraint generation algorithm. We demonstrate the applicability of the proposed approach using several retrospective patient data sets and discuss the computational efficiency and solution quality of the proposed approach for different cases of the algorithm. Our results show that the proposed method decreases the solution time by 75% to 98% for all patients, without affecting the treatment quality compared to the original full-scale IMRT problem.

Dose-based constraint generation for large-scale IMRT optimization