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Minimum MU Optimization (MMO): An Inverse Optimization Approach for the PBS Minimum MU Constraint

H Gao1*, B Clasie2 , T Liu1 , Y Lin1 , (1) Department of Radiation Oncology, Winship Cancer Institute of Emory University, Atlanta, GA, (2) Department of Radiation Oncology, Massachusetts General Hospital and Harvard Medical School, Boston, MA


(Sunday, 7/14/2019) 1:00 PM - 2:00 PM

Room: 302

Purpose: The deliverability of proton pencil beam scanning (PBS) treatment plans is subject to the minimum monitor unit (MU) constraint. This work introduces an inverse optimization approach to enforce the minimum MU constraint on planned spots, for accurate delivery of the planned dose.

Methods: We formulate the minimum MU problem as an inverse optimization problem that accounts for the minimum MU constraint, i.e., minimum MU optimization (MMO). The MMO minimizes the difference between planned dose and deliverable dose while simultaneously enforcing the minimum MU constraint. Owing to the minimum MU constraint, MMO is nonconvex. Iterative convex relaxations are applied so that a sequence of convex subproblems of MMO need to be solved. The solution algorithm to the convex subproblem is developed based on alternating direction method of multipliers. In order to accelerate MMO, truncated spatial grid is used for MMO: doses are only matched during MMO for the voxels with dose no less than 10% of the maximum dose; in addition, three undersampling patterns are explored on the truncated spatial grid: equally-spaced sampling, random sampling, equally-spaced sampling after dose sorting.

Results: The MMO is validated in comparison with a greedy reassignment (GR) algorithm, using representative PBS fields from patient plans optimized using Astroid with spots of various sizes. The γ-index results based on 3D dose calculation suggest MMO can provide more accurate deliverable plans than GR, for various levels of minimum-MU constraints. On the other hand, MMO can be accelerated using 25% data on the truncated spatial grid, i.e., only 5-10% of original dose points are needed for MMO to maintain its accuracy in terms of γ-indexes.

Conclusion: An effective method, namely MMO, based on inverse optimization formulation is developed to postprocess the PBS fields to meet the minimum MU constraint, and accelerated by undersampling on truncated spatial grid.


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