A multicriteria framework with voxel-dependent parameters for radiotherapy treatment plan optimization.
OBJECTIVE
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.
Center for Advanced Radiotherapy Technologies and Department of Radiation Medicine and Applied Sciences, University of California San Diego, La Jolla, California 92037-0843.
Masoud
M
Zarepisheh
Center for Advanced Radiotherapy Technologies and Department of Radiation Medicine and Applied Sciences, University of California San Diego, La Jolla, California 92037-0843.
Andres F
AF
Uribe-Sanchez
Center for Advanced Radiotherapy Technologies and Department of Radiation Medicine and Applied Sciences, University of California San Diego, La Jolla, California 92037-0843.
Nan
N
Li
Center for Advanced Radiotherapy Technologies and Department of Radiation Medicine and Applied Sciences, University of California San Diego, La Jolla, California 92037-0843.
Xun
X
Jia
Center for Advanced Radiotherapy Technologies and Department of Radiation Medicine and Applied Sciences, University of California San Diego, La Jolla, California 92037-0843.
Steve B
SB
Jiang
D006801:Humans; D009369:Neoplasms / Q000532:radiotherapy; D058958:Organs at Risk / Q000528:radiation effects; D011879:Radiotherapy Dosage; D011880:Radiotherapy Planning, Computer-Assisted / Q000379:methods*; D013499:Surface Properties