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Robust Management of Motion Uncertainty in Intensity-Modulated Radiation Therapy

Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114
Operations Research Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, Massachusetts 02114
Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
tbortfeld{at}partners.org
tcychan{at}alum.mit.edu
atrofimov{at}partners.org
jnt{at}mit.edu

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 intensity-modulated 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.
History: Received December 2006; revision received March 2007; accepted April 2007.