Integrating soft and hard dose-volume constraints into hierarchical constrained IMRT optimization

Abstract

Purpose: Dose-volume constraints (DVCs) continue to be common features in intensity-modulated radiation therapy (IMRT) prescriptions, but they are non-convex and difficult to incorporate. We propose computationally efficient methods to incorporate dose-volume constraints (DVCs) into automated IMRT planning. Methods: We propose a two-phase approach: in phase-1, we solve a convex approximation with DVCs. Although this convex approximation does not guarantee DVC satisfaction, it provides crucial initial information about voxels likely to receive doses below DVC thresholds. Subsequently, phase-2 solves an optimization problem with maximum dose constraints imposed on those subthreshold voxels. We further categorize DVCs into hard- and soft-DVCs, where hard-DVCs are strictly enforced by the optimization and soft-DVCs are encouraged in the objective function. We tested this approach in our automated treatment planning system which is based on hierarchical constrained optimization. Performance is demonstrated on a series of paraspinal, lung, oligometastasis, and prostate cases as well as a small paraspinal case for which we can computationally afford to obtain a ground-truth by solving a non-convex optimization problem. Results: The proposed algorithm successfully meets all the hard-DVCs while increasing the overall computational time of the baseline planning process (without DVCs) by 20%, 10%, and 11% for paraspinal, oligometastasis, and prostate cases, respectively. For a soft-DVC applied to the lung case, the dose-volume histogram curve moves toward the desired direction and the computational time is increased by 11%. For a low-resolution paraspinal case, the ground-truth solution process using mixed-integer programming methods required 15 h while the proposed algorithm converges in only 2 min with a proximal solution. Conclusions: A computationally tractable algorithm to handle hard- and soft-DVCs is developed which is capable of satisfying DVCs without any parameter tweaking. Although the algorithm is demonstrated in our in-house developed automated treatment planning system, it can potentially be used in any constrained optimization framework.