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Treatment Plan Optimization for Spatiotemporal Fractionation Schemes with Optimality Bounds

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D Papp

D Papp1*, M Gaddy1 , S Yildiz2 , J Unkelbach3 , (1) North Carolina State University, Raleigh, North Carolina, (2) The Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, North Carolina, (3) University Hospital Zurich, Zurich, Switzerland


TU-D-108-7 (Tuesday, August 1, 2017) 11:00 AM - 12:15 PM Room: 108

Purpose: Spatiotemporal fractionation schemes, i.e., treatments delivering different dose distributions in different fractions, can potentially lower treatment side-effects without compromising tumor control. This can be achieved by hypofractionating parts of the tumor while delivering approximately uniformly fractionated doses to the surrounding tissue. Plan optimization for such treatments is based on biologically-effective dose (BED), however, this leads to computationally challenging non-convex optimization problems. Currently used optimization methods only yield locally optimal solutions and it has been unclear whether these plans are close to the globally best solution. We present an optimization framework to compute rigorous bounds on the maximum achievable normal tissue dose reduction for spatiotemporal fractionation plans.

Methods: The approach is demonstrated on liver tumors, where the primary goal is to reduce mean liver BED without compromising any other treatment objective. First, a conventional, uniformly fractionated, plan is computed. Then a second, non-convex, optimization model is solved to local optimality, to compute a nonuniformly fractionated plan that minimizes mean liver BED, subject to the constraints that the plan is no worse than the uniformly fractionated plan with respect to all other planning goals. Finally a convex relaxation of the second model is solved, which provides a rigorous bound on the global optimal value of the second model, to assess the quality of the local optimal solution.

Results: The computed nonuniform plans achieve 11-34 percent mean liver BED reduction over the optimal uniformly fractionated plans. These nonuniform plans close 75-90 percent of the gap between the bounds on the maximum mean liver BED reduction and the mean liver BED of the uniform plan.

Conclusion: The results indicate that spatiotemporal treatments can achieve substantial reductions in normal tissue dose. Our work further shows that local optimization techniques provide high-quality plans that are close to realizing the maximum potential normal tissue dose reduction.

Funding Support, Disclosures, and Conflict of Interest: This material was based upon work partially supported by the National Science Foundation under Grant DMS-1127914 to the Statistical and Applied Mathematical Sciences Institute.

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