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Radiation therapy is subject to uncertainties that need to be accounted for when determining a suitable treatment plan for a cancer patient. For lung and liver tumors, the presence of breathing motion during treatment is a challenge to the effective and reliable delivery of the radiation. In this paper, we build a model of motion uncertainty using probability density functions that describe breathing motion, and provide a robust formulation of the problem of optimizing intensitymodulated radiation therapy. We populate our model with real patient data and measure the robustness of the resulting solutions on a clinical lung example. Our robust framework generalizes current mathematical programming formulations that account for motion, and gives insight into the trade-off between sparing the healthy tissues and ensuring that the tumor receives sufficient dose. For comparison, we also compute solutions to a nominal (no uncertainty) and margin (worst-case) formulation. In our experiments, we found that the nominal solution typically underdosed the tumor in the unacceptable range of 6% to 11%, whereas the robust solution underdosed by only 1% to 2% in the worst case. In addition, the robust solution reduced the total dose delivered to the main organ-at-risk (the left lung) by roughly 11% on average, as compared to the margin solution.
Subject classifications: linear programming: applications; health care: treatment.
Area of review: Special Issue on Operations Research in Health Care.
History: Received December 2006; revision received March 2007; accepted April 2007.
1. Introduction
For the year 2006, the American Cancer Society (2006) estimated that there would be roughly 1.4 million new cases of cancer and 550,000 cancer deaths in the United States. Overall, cancer accounts for roughly 25% of all deaths in the United States. Even in comparison to other cancers, lung cancer stands out as particularly deadly and difficult to treat. Although the incidence of lung cancer is falling due to the decreasing prevalence of smoking, it is still by far the leading cause of cancer-related death in both men and women, accounting for roughly 29% of all cancer deaths. It outpaces the second leading causes of cancer death, which are prostate/colorectal cancer for men and breast cancer for women, by a factor of roughly three and two, respectively. As we will describe below, we will...