Mathematical Formulation of DMH-Based Inverse Optimization - Mihaylov, Ivaylo B.; Moros, Eduardo G. (Frontiers in Oncology, 2014)
Purpose: To introduce the concept of dose-mass based inverse optimization for radiotherapy applications. Materials and Methods: Mathematical derivation of the dose-mass based formalism 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 presented. The phantom consists of three regions: a target surrounded by high and low density regions. The target is irradiated with two beams through those regions and inverse optimization with dose-volume and dose-mass based objective functions is performed. The basic properties of the two optimization types are demonstrated on the phantom. Results: It is demonstrated that dose-volume optimization is a special case of dose-mass optimization. In a homogenous media dose-mass optimization turns into dose-volume optimization. The dose calculations performed on the digital phantom show that in this very simple case dose-mass optimization tends to penalize more the dose delivery through the high density region and therefore it results in delivering more dose through the low density region. Conclusions: It was demonstrated that dose-mass based optimization is mathematically more general than dose-volume based optimization. In the case of constant density media dose-mass optimization transforms into dose-volume optimization.