An automated bi‐level optimization approach for IMRT

Abstract

Intensity-modulated radiation therapy is used worldwide to treat cancer patients. The objective of this treatment is to deliver a prescribed radiation dose to the tumor while sparing, as much as possible, all the healthy tissues, especially organs at risk (OAR). This means that the planning of a radiotherapy treatment should take into consideration conflicting objectives: to be able to spare as much as possible the OAR guaranteeing, at the same time, that the desired radiation is delivered to the volumes to treat. While the volumes to treat can be adequately irradiated from almost any set of directions, the radiation directions that are chosen have a determinant impact on the OAR. This means that those directions that provide an improved OAR sparing should be selected. The choice of radiation directions (beam angles) can thus be interpreted as being fundamentally determined by the OAR, with the radiation intensities associated with each of these directions being determined by the needed radiation to be delivered to the volumes to treat. In this work, we interpret the radiotherapy treatment planning problem as a bi-level optimization problem. At the upper level, OAR control the choice of the beam angles, which are selected aiming at OAR sparing. At the lower level, the optimal radiation intensities are decided by the volumes to treat, considering the beam angle ensemble obtained at the upper level. The proposed bi-level approach was tested using 10 clinical head-and-neck cancer cases already treated at the Portuguese Institute of Oncology in Coimbra.

Coordinating harvest planning and scheduling in an agricultural supply chain through a stochastic bilevel programming

“…For example, see Alekseeva et al (2017), Angelo and Barbosa (2015), Bard (2013), Colson et al (2005), and Kalashnikov et al (2015). The applications of bilevel optimization models are suited to coordinate decisions in hierarchical supply chains, as we discussed in the previous section, as well as in finance problems (Jing et al, 2022), transportation systems (Constantin and Florian, 1995), vehicle routing problems , cutting stock problems in industrial processes (Andrade et al, 2016), facility locations problems (Camacho-Vallejo et al, 2014), radiation therapy (Carrasqueira et al, 2023), optimal allocation of a water system , and emergency evacuation planning (Ng et al, 2010), among other fields of application (Sinha et al, 2017).…”