Estimation theory and model parameter selection for therapeutic treatment plan optimization

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. (C) 1999 American Association of Physicists in Medicine. [S0093-2405(99)01011-1].