An optimization algorithm for intensity modulated radiotherapy--the simulated dynamics with dose-volume constraints

We have developed a new method for optimization in intensity modulated radiation therapy (IMRT) that makes use of simulated dynamics in a classical system of interacting particles. An analogy is drawn between intensity profile optimization in IMRT and relaxation to the equilibrium configuration in a dynamic system. The intensities of beamlets are equivalent to the positions of the virtual particles. The potential energy of the system is defined by the objective function, which determines the equations of motion for the virtual particles. In this paper, we present the implementation of dose constraints and dose-volume constraints. Our strategy is to optimize the dose to the planned target volume (PTV) while keeping all constraints to the organs at risk (OARs) satisfied rigorously. A simple quadratic objective function is used that only includes terms for PTV voxels. By this approach, no additional parameters other than that for prescribing desired dose and constraints, such as importance factors, are needed. The hard constraints that require non-negative beamlet intensities and that the dose at any voxel in an OAR cannot exceed a maximum tolerance, are implemented as semi-transmittable potential barriers of infinite height. Dose-volume constraints are handled by placing hard constraints on partial volumes. Handling of the clinically applied constraints was tested using phantoms and clinical cases. Our results show that the dose-volume histogram (DVH) type of plan prescription can be fulfilled with satisfactory PTV coverage. In addition to the convenience of implementation, our method can achieve a high computational efficiency with the understanding of the dynamic behavior of the system.