A multicriteria framework with voxel‐dependent parameters for radiotherapy treatment plan optimization

Abstract

Purpose: To establish a new mathematical framework for radiotherapy treatment optimization with voxel-dependent optimization parameters. Methods: In the 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 a set of the objective functions associated to the 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. Furthermore, questions about the objective function selection and parameter adjustment to assure Pareto optimality as well as the relationship between the optimal solutions obtained from the organ-based and voxel-based models remain unanswered. To answer these questions, the authors establish in this work a new mathematical framework equipped with two theorems. Results: 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 impact of using different objective functions on plan qualities and Pareto surfaces. 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 Pareto surface is independent of the objective function selection and the entire Pareto surface could be generated as long as the objective function satisfies certain mathematical conditions; (2) All Pareto solutions generated by the organ-based model with different objective functions are parts of a unique Pareto surface generated by the voxel-based model with any appropriate objective function; (3) A much 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. Conclusions:The authors have developed a mathematical framework for radiotherapy treatment optimization using voxel-based parameters. The authors can improve the plan quality by adjusting voxel-based weighting factors and exploring the unique and large Pareto surface which include all the Pareto surfaces that can be generated by organ-based model using different objective functions.

A DVH-guided IMRT optimization algorithm for automatic treatment planning and adaptive radiotherapy replanning

“…In contrast, an objective function selection is no longer an issue in the voxel-based is generated by the voxel-based model as long as the penalty function F satisfies some desirable properties. The dose distribution Pareto surface is much larger than the organ-based Pareto surfaces, and in our previous work 38 we proved that it encompasses all the Pareto surfaces generated by the organbased model using different penalty functions. We also proved that it includes all the plans which are Pareto optimal in terms of the DVH concept.…”

“…For details readers are referred to Ref. 38. Problems (1) and (2) illustrate the general form of the voxel-based and the organ-based optimization models, respectively,…”

“…In order to get the feasible and infeasible sets of the DVHs, we first generated a plan by solving Problem (3) with a set of the weighting factors, which yields a plan that is Pareto optimal in terms of the DVHs, 38 and then we manipulated them. An infeasible plan can be obtained by improving the DVH curves of the Pareto optimal plan (shifting the OAR DVHs toward left and PTV DVH toward prescription dose), and a feasible plan can be generated by worsening the DVHs of the Pareto optimal plan.…”

“…We recently did a mathematical study on the voxel-based model that revealed the main advantages of this model. 38 However, the adjustment of a dramatically increased number of parameters (voxel weights) in the voxel-based model remained to be a big problem, which makes the trial-and-error approach of parameter selection impossible to apply clinically. We propose a systematic scheme to adjust the voxel weights automatically in order to approach the reference DVHs.…”

Physically constrained voxel‐based penalty adaptation for ultra‐fast IMRT planning

“…(5,7–17 ) Recently Zarepisheh et al (18) explained the mathematical foundation of these algorithms. For the purpose of this paper, we identify two different classes of adaptation strategies.…”