A linear optimization model for high dose rate brachytherapy using a novel distance metric.

We propose a linear network-based optimization model (LNBM) for high dose rate brachytherapy (HDR-BT) that uses a novel distance metric to measure the discrepancy between the dose delivered and the prescription. Unlike models in the literature, LNBM takes advantage of the adjacency structure of the patients' voxels by formalizing them into a network.We apply LNBM to a set of 7 cervical cancer cases treated with HDR-BT. State-of-the-art commercial optimization software solves LNBM to global optimality. The results of LNBM are compared with those of inverse planning by simulated annealing (IPSA) based on tumor coverage, dosimetric indices for the critical organs at risk (OARs), isodose contour plots, and two metrics of homogeneity new to this work (hot-spots volumes and diameters).LNBM produces plans with improved tumor coverage and with improved isodose contour plots and dosimetric indices for OARs that receive highest dose (bladder and rectum in this study) when compared with IPSA. Using new metrics of homogeneity, we also demonstrate that LNBM produces more homogeneous plans on these cases. An analysis of the solutions of LNBM shows that they use a significant part of the voxel network structure, providing evidence that the plans produced are different from those created using traditional penalty approaches and are more directly guided by the geometry of the patients' anatomy.The proposed linear network-based optimization model efficiently generates more homogeneous high quality treatment plans for HDR-BT.