Dynamic Restricted Column Generation in MIQP for Cancer Radiation Therapy

More than 14 million new cases of cancer are diagnosed globally each year, with approximately 50% of all cancer patients receiving radiation therapy during the course of their disease. Advanced technology using a multi-leaf collimator can deliver non-uniform radiation doses that best conform to the tumor shape while sparing the surrounding normal tissues. Combinatorically, selecting beam angles is computationally taxing and remains a major challenge. Consequently, clinical systems opt to use preselected angles without integrating a combinatorial computational engine within the fluence map optimization process.In this paper, we offer a mixed integer quadratic programming optimization approach to simultaneously determine optimal beam angles and fluence maps. For computational efficiency, a dynamic restricted branch-and-price method is derived to solve these large-scale patient instances. Clinical analyses of prostate and head-and-neck cancer patient cases show that our approach yields treatment plans that are far superior to current best practice in the clinical environment. Specifically, the resulting plans achieve better conformity and homogeneity to the tumor while reducing radiation exposure to the critical structures. Computationally, besides drastically reducing the solution time, the dynamic restricted branch-and-price method provides an additional bonus: every node consists of only a relatively small number of beam variables in the branch-and-bound framework. This implies that in the middle of the solution process, a feasible and clinically acceptable treatment plan is available, and can be obtained by taking a few branching steps on the beam variables that are in the active set.