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Estimation theory and model parameter selection for therapeutic treatment plan optimization
Author(s) -
Xing L.,
Li J. G.,
Pugachev A.,
Le Q. T.,
Boyer A. L.
Publication year - 1999
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 - 10.1118/1.598749
Subject(s) - mathematical optimization , computer science , estimator , optimization problem , generality , inverse problem , mathematics , algorithm , statistics , psychology , mathematical analysis , psychotherapist
Treatment optimization is usually formulated as an inverse problem, which starts with a prescribed dose distribution and obtains an optimized solution under the guidance of an objective function. The solution is a compromise between the conflicting requirements of the target and sensitive structures. In this paper, the treatment plan optimization is formulated as an estimation problem of a discrete and possibly nonconvex system. The concept of preference function is introduced. Instead of prescribing a dose to a structure (or a set of voxels), the approach prioritizes the doses with different preference levels and reduces the problem into selecting a solution with a suitable estimator. The preference function provides a foundation for statistical analysis of the system and allows us to apply various techniques developed in statistical analysis to plan optimization. It is shown that an optimization based on a quadratic objective function is a special case of the formalism. A general two‐step method for using a computer to determine the values of the model parameters is proposed. The approach provides an efficient way to include prior knowledge into the optimization process. The method is illustrated using a simplified two‐pixel system as well as two clinical cases. The generality of the approach, coupled with promising demonstrations, indicates that the method has broad implications for radiotherapy treatment plan optimization.