Application of optimization model with piecewise penalty to intensity-modulated radiation therapy

Purpose: Both maximum-dose-based and generalized equivalent uniform dose (gEUD)-based quadratic sub-scores, which penalize doses higher than the prescribed dose, exhibit the shortcomings of semi-deviation and a vanishing gradient in the feasible solution space. To address these drawbacks, this study proposes new sub-scores for the maximum dose criterion and the gEUD criterion. Methods: In new sub-scores, a dosage lower than the prescribed dose is assigned a linear penalty function, and one higher than the prescribed dose is assigned an extra quadratic penalty function. To test their efficiency, they were incorporated into a physical model and a hybrid physical-biological model, respectively, and were tested on a phantom TG119 and two types of clinic cases. The improved methods were compared with their original methods and the dose-volume (DV)-based optimization method. Additionally, the improved gEUD-based method was compared with another gEUD-based quadratic optimization method. The gradient-based optimization algorithm was applied to solve these large-scale optimization problems. Results: For similar or better PTV coverage, optimization based on our proposed quadratic models is capable of improving the OARs sparing. In practice, by using multiple DV constraints for each optimized structures, the DV based optimization may be able to arrive at similar plan, whereas greater trial-and-error is performed to adjust parameters of optimization model. Although the optimal prescribed dose remains unclear, at the same prescribed dose, our proposed optimization method can obtain better plan. Conclusion: Our proposed optimization method has the potential to expand the solution space and improve the quality of radiotherapy plan.