Effective optimization strategy for large optimization volume object, remaining volume at risk (RVR): α-value selection and usage from generalized equivalent uniform dose (gEUD) curve deviation perspective

Objective.A large optimization volume for intensity-modulated radiation therapy (IMRT), such as the remaining volume at risk (RVR), is traditionally unsuitable for dose-volume constraint control and requires planner-specific empirical considerations owing to the patient-specific shape. To enable less empirical optimization, the generalized equivalent uniform dose (gEUD) optimization is effective; however, the utilization of parametera-values remains elusive. Our study clarifies thea-value characteristics for optimization and to enable effectivea-value use.Approach.The gEUD can be obtained as a function of itsa-value, which is the weighted generalized mean; its curve has a continuous, differentiable, and sigmoid shape, deforming in its optimization state with retained curve characteristics. Using differential geometry, the gEUD curve changes in optimization is considered a geodesic deviation intervened by the forces between deforming and retaining the curve. The curvature and gradient of the curve are radically related to optimization. The vertex point (a=a_k) was set and thea-value roles were classified into the following three parts of the curve with respect to thea-value: (i) high gradient and middle curvature, (ii) middle gradient and high curvature, and (iii) low gradient and low curvature. Then, a strategy for multiplea-values was then identified using RVR optimization.Main results.Eleven head and neck patients who underwent static seven-field IMRT were used to verify thea-value characteristics and curvature effect for optimization. The lowera-value (i) (a= 1-3) optimization was effective for the whole dose-volume range; in contrast, the effect of highera-value (iii) (a= 12-20) optimization addressed strongly the high-dose range of the dose volume. The middlea-value (ii) (arounda=a_k) showed intermediate but effective high-to-low dose reduction. Thesea-value characteristics were observed as superimpositions in the optimization. Thus, multiple gEUD-based optimization was significantly superior to the exponential constraints normally applied to the RVR that surrounds the PTV, normal tissue objective (NTO), resulting in up to 25.9% and 8.1% improvement in dose-volume indices D2% and V10Gy, respectively.Significance.This study revealed an appropriatea-value for gEUD optimization, leading to favorable dose-volume optimization for the RVR region using fixed multiplea-value conditions, despite the very large and patient-specific shape of the region.