A convex optimization approach to radiation treatment planning with dose constraints

We present a method for handling dose constraints as part of a convex programming framework for inverse treatment planning. Our method uniformly handles mean dose, maximum dose, minimum dose, and dose-volume (i.e., percentile) constraints as part of a convex formulation. Since dose-volume constraint...

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Bibliographic Details
Published in:Optimization and engineering 2019-03, Vol.20 (1), p.277-300
Main Authors: Fu, Anqi, Ungun, Barıṣ, Xing, Lei, Boyd, Stephen
Format: Article
Language:English
Subjects:
Computational geometry
Construction planning
Control
Convexity
Engineering
Environmental Management
Financial Engineering
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Radiation dosage
Radiation therapy
Research Article
Slack variables
Source code
Systems Theory
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Summary:We present a method for handling dose constraints as part of a convex programming framework for inverse treatment planning. Our method uniformly handles mean dose, maximum dose, minimum dose, and dose-volume (i.e., percentile) constraints as part of a convex formulation. Since dose-volume constraints are non-convex, we replace them with a convex restriction. This restriction is, by definition, conservative; to mitigate its impact on the clinical objectives, we develop a two-pass planning algorithm that allows each dose-volume constraint to be met exactly on a second pass by the solver if its corresponding restriction is feasible on the first pass. In another variant, we add slack variables to each dose constraint to prevent the problem from becoming infeasible when the user specifies an incompatible set of constraints or when the constraints are made infeasible by our restriction. Finally, we introduce ConRad, a Python-embedded open-source software package for convex radiation treatment planning. ConRad implements the methods described above and allows users to construct and plan cases through a simple interface.
ISSN:1389-4420
1573-2924
DOI:10.1007/s11081-018-9409-2