Biological Planning for High-Dose-Rate Brachytherapy: Application to Cervical Cancer Treatment

Cervical cancer has a high mortality rate (approximately 35 percent) in the United States and is difficult to treat successfully. One promising treatment is high-dose-rate brachytherapy, which entails delivering high-dose radiation to the tumor via the temporary implantation of radioactive seeds. This treatment promises to be particularly effective in eradicating tumors while preserving the organs. Yet, major obstacles to successful treatment remain, especially (1) determining the best seed type, spatial configuration of seeds, and seed dwelling time, and (2) improving the probability that the treatment will eliminate all malignant cells. We developed an advanced planning model to simultaneously address both of these issues. To permit taking advantage of the best available information, our model works with inputs from positron emission tomography. We begin with a multiobjective, nonlinear, mixed-integer programming model that is initially intractable. To solve the model, we introduce an original branch-and-cut and local-search approach that couples new polyhedral cuts with matrix reduction and intelligent geometric heuristics. The result has been accurate solutions that are obtained rapidly. Clinical trials at Rush University Medical Center demonstrated superior medical outcomes. These analytical techniques are applicable not only to cervical cancer, but also to other types of cancer, including breast, lung, and prostate cancer.