Frontiers in Oncology (Jul 2014)
Mathematical Formulation of Energy Minimization - Based Inverse Optimization
Abstract
Purpose: To introduce the concept of energy minimization based inverse optimization for external beam radiotherapy.Materials and 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 regions: 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 delivery somewhat higher maximum doses compared to standard of care, realized with dose-volume based optimization. At the same time however the energy minimization optimization reduces much more significantly the average and the integral doses.
Keywords
