Timothy Chan

Operations Research Center,

Massachusetts Institute of Technology

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 poster, we present a model of motion uncertainty using probability density functions that describe breathing motion, and provide a robust formulation to optimize a particular type of therapy known as intensity-modulated radiation therapy.  We populate our model with real patient data from Massachusetts General Hospital and measure the robustness of the resulting solutions on a clinical lung case.  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.  An intensity map that results from our robust optimization approach will balance intensity-modulation with intensity-homogeneity in order to effectively address this trade-off.  Accordingly, our approach implicitly performs multi-objective optimization on these competing objectives.

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.  Our results suggest that we may add robustness -- which improves tumor coverage in the face of uncertainty -- to current treatment protocols, while incurring minimal cost in terms of additional dose to the healthy tissue.