TH-A-213AB-06: Investigation and Evaluation of Two-Point Step-Size Gradient Methods for IMRT/VMAT Treatment Plan Optimization

Abstract

Purpose: To investigate and evaluate fast two-point step-size gradient methods for IMRT/VMAT treatment plan optimization with nonlinear convex models. Methods: Commonly applied optimization models for IMRT/VMAT planning are nonlinear and convex, including many quadratic physical models and general nonlinear biological models. The solutions are typically found through gradient-based algorithms. Existing methods, however, suffer from the low efficiency of the line search process. In this work, we investigate the use of two-point step-size gradient methods for solving general nonlinear convex models in IMRT/VMAT planning. With such algorithms, the line search step can be avoided or highly reduced, and significant speedup can be obtained. As a specified form of nonlinear convex models, the quadratic models are particularly investigated and the best form of the gradient method without line search is found. Results: Five clinical prostate and five clinical head-and-neck cancer cases were tested for both IMRT and VMAT planning. For general nonlinear convex models, the Modified Two-Point Step-Size Gradient Method was found to have the best efficiency: for all test cases, approximately 5 times speedup was obtained with similar convergence properties compared to the traditional line search method. For quadratic models, the original Barzilai-Borwein method offered the best performance: for all test cases, approximately 10 times speedup was obtained with better convergence properties (i.e., better treatment quality). For instance, for typical prostate cancer cases with a penalty-based quadratic model, it takes ∼4 seconds to generate optimized 9-beam fluence maps compared to ∼40 seconds using traditional line search method on a PC. Conclusions: This work provides a guideline to speedup IMRT/VMAT treatment plan optimization for general nonlinear convex models without loss of treatment quality. The current experiments were all run on CPU. Based on our previous experience, additional 10–30 times speedup can be expected with GPU–based implementation.