A Column Generation Approach Based on Region Growth

In intensity-modulated radiation therapy (IMRT), a network flow is adopted to solve the pricing problem of the generic column generation approach in order to obtain a deliverable aperture. However, excessive computation results from the direct use of a network flow. In addition, a decline in plan quality may result from the direct determination of the leaf position using the gradient information. To overcome these problems, a column generation approach based on region growth is proposed. The proposed method is designed to reduce the computational cost of solving the pricing problem and improve the IMRT plan quality. First, the gradients of the beamlets are obtained by an objective function constructed under the constraint conditions of the organs. Second, the gradients are transformed nonlinearly. Third, the positions of the continuous negative gradient regions in each row of the aperture are determined and stored. Fourth, these gradients are taken as a whole and added to the aperture network flow, which is solved as a shortest-path problem. Finally, the deliverable aperture is obtained and added to the treatment plan. To verify the effectiveness of the proposed method, experiments involving five five-field prostate cancer cases and five nine-field head and neck cancer cases were conducted. Compared with the generic column generation method, the dose distribution of the target is ensured by the proposed method, which also effectively protects organs at risk and reduces the running time. Specifically, in ten groups of comparative experiments, the normal tissue complication probability of the proposed method is reduced by up to 3.37%, and the maximum acceleration rate is 20.44%. According to the experimental results, the proposed method is more consistent with clinical requirements compared with the generic column generation method.