Effective optimization strategy for large optimization volume object, remaining volume at risk (RVR): -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 parameter a-values remains elusive. Our study clarifies the a-value characteristics for optimization and to enable effective a-value use. Approach. The gEUD can be obtained as a function of its a-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 the a-value roles were classified into the following three parts of the curve with respect to the a-value: (i) high gradient and middle curvature, (ii) middle gradient and high curvature, and (iii) low gradient and low curvature. Then, a strategy for multiple a-values was then identified using RVR optimization. Main results. Eleven head and neck patients who underwent static seven-field IMRT were used to verify the a-value characteristics and curvature effect for optimization. The lower a-value (i) (a = 1-3) optimization was effective for the whole dose-volume range; in contrast, the effect of higher a-value (iii) (a = 12-20) optimization addressed strongly the high-dose range of the dose volume. The middle a-value (ii) (around a = a ( k )) showed intermediate but effective high-to-low dose reduction. These a-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 appropriate a-value for gEUD optimization, leading to favorable dose-volume optimization for the RVR region using fixed multiple a-value conditions, despite the very large and patient-specific shape of the region.