title: Mathematical formulation of energy minimization - based inverse optimization.
abstract: OBJECTIVE
  To introduce the concept of energy minimization-based inverse optimization for external beam radiotherapy.
  
  
  METHODS
  Mathematical formulation of energy minimization-based inverse optimization is presented. This mathematical representation is compared to the most commonly used dose-volume based formulation used in inverse optimization. A simple example on digitally created phantom is demonstrated. The phantom consists of three sections: a target surrounded by high and low density regions. The target is irradiated with two beams passing through those regions. Inverse optimization with dose-volume and energy minimization-based objective functions is performed. The dosimetric properties of the two optimization results are evaluated.
  
  
  RESULTS
  Dose-volume histograms for all the volumes of interest used for dose optimization are compared. Energy-based optimization results in higher maximum dose to the volumes that are used as dose-limiting structures. However, the average and the integral doses delivered for the volumes outside of the target are larger with dose-volume optimization.
  
  
  CONCLUSIONS
  Mathematical formulation of energy minimization-based inverse optimization is derived. The optimization applied on the digital phantom shows that energy minimization-based approach tends to deliver somewhat higher maximum doses compared to standard of care, realized with dose-volume based optimization. At the same time, however, the energy minimization-based optimization reduces much more significantly the average and the integral doses.
authors.affiliation: Department of Radiation Oncology, University of Miami , Miami, FL , USA.
authors.forename: Ivaylo B
authors.initials: IB
authors.lastname: Mihaylov
keywords: dose; energy; integral dose; inverse optimization; mass; volume
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