Robust Management of Motion Uncertainty in Intensity-Modulated Radiation Therapy

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 (worstcase) formulation. Unlike the nominal solution, which delivered an unacceptable 6% average underdose to the tumor in our 78 test cases, the robust solution resulted in only a 1% worst-case underdose. 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.