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MO‐D‐351‐08: Analysis of the Effects of Multiple GEUD‐Type Constraints On Dose Distribution for IMRT Optimization
Author(s) -
Zinchenko Y,
Craig T,
Keller H,
Terlaky T,
Sharpe M
Publication year - 2008
Publication title -
medical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.473
H-Index - 180
eISSN - 2473-4209
pISSN - 0094-2405
DOI - 10.1118/1.2962359
Subject(s) - mathematics , mathematical optimization , convex optimization , moment (physics) , random variable , histogram , regular polygon , distribution (mathematics) , algorithm , computer science , statistics , artificial intelligence , mathematical analysis , image (mathematics) , physics , geometry , classical mechanics
Purpose: To analyze the effects of multiple gEUD‐type (convex) constraints on the resulting dose‐volume distribution/histogram (DVH). A key motivation for this work is to find a convex optimization alternative to (non‐convex) partial volume constraints in IMRT optimization. Method and Materials: A formal mathematical framework for analysis of the effects of multiple gEUD‐type constraints on the resulting DVH is proposed. The framework relies on interpreting DVH as a cumulative probability distribution of the underlying “random”, i.e., unknown variable, representing dose to a voxel. Consequently, the analysis of the effects of gEUD‐based constraints on DVH is rephrased in terms of the effects of moments of the random variable on its distribution, which corresponds to a well‐recognized moment problem in mathematics. Results: Given a set of gEUD‐type constraints, we demonstrate how to compute the worst —in a sense of generating the largest volume ratio receiving a fixed dose— dose‐volume distributions that satisfy these constraints. A generalization of gEUD‐based constraints, the Generalized Moment Constraints (GMC's), is proposed, with the rationale behind GMC's to provide more modeling flexibility for IMRT optimization. A potential applicability of the approach is discussed. Applicability analysis is based on proximity of a family of dose distributions, satisfying a fixed set of GMC's, to the desired “ideal” dose distribution. We use a hypothetical prostate cancer patient's rectum as an example. Conclusion: The newly proposed convex GMC‐based dose‐distribution modeling framework has a potential to serve as a viable alternative to partial volume constraints in IMRT optimization, at least for some critical structures. To name a few potential benefits of our approach, we mention global solution to IMRT optimization problem that minimizes proximity of a physically deliverable plan to the desired “ideal” physician‐prescribed plan, and better control over the resulting dose distributions. Further investigation of the approach is required and is ongoing.