Robust Management of Motion Uncertainty in Intensity-Modulated Radiation Therapy

• Published in: Operations research Vol. 56; no. 6; pp. 1461 - 1473
• Main Authors: Bortfeld, Thomas, Chan, Timothy C. Y, Trofimov, Alexei, Tsitsiklis, John N
• Format: Journal Article
• Language: English
• Published: Linthicum INFORMS 01.11.2008; Institute for Operations Research and the Management Sciences
• Subjects: Anatomy; applications; Breathing; Cancer; Cancer therapies; Care and treatment; Collaboration; Comparative analysis; Dosimetry; Health aspects; health care; Intensity-modulated radiotherapy; Linear programming; Lung cancer; Lungs; Mathematical programming; Objective functions; Operations research; Optimal solutions; Planning; Prostate; Radiation oncology; Radiation therapy; Radiotherapy; Robust optimization; Studies; Time & motion studies; treatment; Tumors; Working groups; United States; United States > US
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1070.0484

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.