A Novel Reduced-Order Prioritized Optimization Method for Radiation Therapy Treatment Planning

In this study, a novel reduced order prioritized algorithm is presented for optimization in radiation therapy treatment planning. The proposed method consists of three stages. In the first stage, the intensity space was sampled by solving a series of unconstrained optimization problems. The objective function of the first stage is expressed as a scalarized weighted sum of partial objectives for the target and organ at risk. Latin hypercube sampling was utilized to define the weights for each run of the unconstrained optimizations. In the second stage, principal component analysis is applied to the solutions determined in the first stage to identify the major eigen modes in the intensities space, significantly reducing the number of independent variables. In the third stage, treatment planning goals/objectives are prioritized, and the problem is solved in the reduced order space. After each objective is optimized, that objective function is converted into a constraint for the lower-priority objectives. In the current formulation, a slip factor is used to relax the hard constraints for planning target volume (PTV) coverage. The applicability of the proposed method is demonstrated for one prostate and one lung intensity-modulated radiation therapy treatment plan. Upon completion of the sequential prioritized optimization, the mean dose at the rectum and bladder was reduced by 21.3% and 22.4%, respectively. Additionally, we investigated the effect of the slip factor `s´ on PTV coverage and we found minimal degradation of the tumor dose (~4%). Finally, the speed up factors upon the dimensionality reduction were as high as 49.9 without compromising the quality of the results.