Mathematical formulation of DMH-based inverse optimization

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. Conclusion: 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.