Nonlinear Continuous Method for Non-Negatively Constrained Inverse Problem of IMRT Planning
Y Tanaka1,2*, K Fujimoto3, T Yoshinaga3, (1) Graduate School of Health Sciences, The University of Tokushima, Japan, (2) Japanese Red Cross Society Kyoto Daiichi Hospital, Japan, (3) Institute of Health Biosciences, The University of Tokushima, JapanSU-E-T-661 Sunday 3:00PM - 6:00PM Room: Exhibit Hall
Purpose: The intensity-modulated radiation therapy (IMRT) is an effective therapeutic technique for the treatment of tumors in the human body without inflicting serious damage to normal tissues. IMRT plans include an optimization strategy for minimizing an objective function of radiation beam weights. We present a novel approach for solving non-negatively constrained inverse problems in IMRT treatment planning, based on the idea of continuous-time dynamical methods using nonlinear differential equations. Our method can compute a feasible solution without the second derivative of an objective function, which is required for gradient-based optimization algorithms such as conjugate gradient and steepest descent methods.
Methods: We first consider the stability of an equilibrium, which corresponds to the desired planning in the IMRT system, by the use of Lyapunov's stability theorem. Then we perform some phantom experiments using phantom data simulating a clinical setup.
Results: We prove theoretically that a Kullback-Leibler (KL) divergence can be a Lyapunov function for the IMRT planning system, in consistent case. It means that the KL-divergence measure decreases along the solution to the differential equation. Additionally, we show that the intensity of any radiation beam is not negative. Because the planning system can be created as an analog electronic circuit, its implementation in actual hardware yields dramatically faster planning as a physical phenomenon with real parallel computing, than software-based iterative methods.
Conclusion: The proposed method provides not only the reduction of a computational cost but also no production of a solution with an unphysical negative radiation beam coefficient in solving IMRT planning inverse problems. Moreover the theoretical results on convergence properties of solutions are confirmed by numerical experiments. Based on the results, we found that we can obtain a feasible solution violating the physical dose constraints minimally, even if the system is inconsistent.