A Multi-Criteria Framework with Voxel-Dependent Parameters for Radiotherapy Treatment Plan Optimization

Abstract: In a treatment plan optimization problem for radiotherapy, a clinically acceptable plan is usually generated by an optimization process with weighting factors or reference doses adjusted for organs. Recent discoveries indicate that adjusting parameters associated with each voxel may lead to better plan quality. However, it is still unclear regarding the mathematical reasons behind it. To answer questions related to this problem, we establish in this work a new mathematical framework equipped with two theorems. The new framework clarifies the different consequences of adjusting organ-dependent and voxel-dependent parameters for the treatment plan optimization of radiation therapy, as well as the different effects of adjusting weighting factors versus reference doses in the optimization process. The main discoveries are threefold: 1) While in the organ-based model the selection of the objective function has an impact on the quality of the optimized plans, this is no longer an issue for the voxel-based model since the entire Pareto surface could be generated regardless the specific form of the objective function as long as it satisfies certain mathematical conditions; 2) A larger Pareto surface is explored by adjusting voxel-dependent parameters than by adjusting organ-dependent parameters, possibly allowing for the generation of plans with better trade-offs among different clinical objectives; 3) Adjusting voxel weighting factors is preferred to adjusting the voxel reference doses since the Pareto optimality can be maintained.