In radiation therapy planning, uncertainties in the definition of the target volume yield a risk of underdosing the tumor. The traditional corrective action in the context of external beam radiotherapy (EBRT) expands the clinical target volume (CTV) with an isotropic margin to obtain the planning target volume (PTV). However, the EBRT-based PTV concept is not directly applicable to brachytherapy (BT) since it can lead to undesirable dose escalation. Here, we present a treatment plan optimization model that uses worst-case robust optimization to account for delineation uncertainties in interstitial high-dose-rate BT of the prostate. A scenario-based method was developed that handles uncertainties in index sets. Heuristics were included to reduce the calculation times to acceptable proportions. The approach was extended to account for delineation uncertainties of an organ at risk (OAR) as well. The method was applied on data from prostate cancer patients and evaluated in terms of commonly used dosimetric performance criteria for the CTV and relevant OARs. The robust optimization approach was compared against the classical PTV margin concept and against a scenario-based CTV margin approach. The results show that the scenario-based margin and the robust optimization method are capable of reducing the risk of underdosage to the tumor. As expected, the scenario-based CTV margin approach leads to dose escalation within the target, whereas this can be prevented with the robust model. For cases where rectum sparing was a binding restriction, including uncertainties in rectum delineation in the planning model led to a reduced risk of a rectum overdose, and in some cases, to reduced target coverage.

Brachytherapy, Delineation uncertainties, Mixed-integer linear optimization, Robust optimization, Treatment planning
INFORMS Journal on Computing
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

Balvert, M, den Hertog, D, & Hoffmann, A.L. (2019). Robust optimization of dose-volume metrics for prostate HDR-brachytherapy incorporating target and OAR volume delineation uncertainties. INFORMS Journal on Computing, 31(1), 100–114. doi:10.1287/ijoc.2018.0815