Effective heuristics for beam angle optimization in radiation therapy

Abstract

In radiation therapy, the main challenge is to deliver the dose to the tumor while sparing healthy tissues around the tumor. One important decision to make is the beam configuration. The corresponding mathematical problem, known as beam angle optimization (BAO), is a large-scale problem. We propose three novel heuristic approaches to reduce the computation time and find high-quality treatment plans for BAO. The first heuristic is based on the fact that the beams that are geometrically close to each other (i.e., ‘adjacent’ beams) have similar impacts, and hence are less likely to be used in the optimal configuration simultaneously. Therefore, in this heuristic, referred to as ‘neighbor cuts’, their use is limited. The second heuristic is to eliminate the beams with small contribution to dose delivery in the ideal plan when all candidate beams can be used. Finally, the number of beams is reduced in the third heuristic while ensuring the quality of the plan remains within a pre-specified range. These heuristics can be applied to any formulation for BAO for various external radiation therapy techniques. We evaluate these heuristics by applying them to a mixed integer programming (MIP) formulation of BAO for a phantom liver case and a clinical liver case.