Practical gEUD optimization technique for stereotactic radiation therapy based on a theoretical reinterpretation using the gEUD curve concept.

Objective.The generalized equivalent uniform dose (gEUD) is a well-established metric for radiotherapy dose optimization, particularly for normal tissues. However, the lack of theoretical clarity in its application has often led to empirical use in clinical practice. This study aims to reformulate gEUD-based optimization in a theoretical framework using the gEUD curve concept, and to develop a robust optimization strategy tailored for stereotactic radiation therapy (SRT), with a specific focus on bone and spinal metastases.Approach.We interpreted the gEUD as a smooth function of itsa-parameter, forming a continuous curve whose deformability decreases with increasinga. Based on this understanding, we proposed two methods: the multiple gEUD objective (MgEUDO) for optimizing the remaining volume at risk, and the selective gEUD objective (SgEUDO) for critical organs at risk. These methods were retrospectively evaluated in 22 patients who received five-fraction SRT (35 Gy total prescription).Main results.Using consistent gEUD-based optimization, all cases achieved clinically favorable dose distributions. Compared to conventional normal tissue objective constraints, the proposed strategy reduced mean dose to surrounding tissues by 10%, while improving tumor dose coverage by 0.6%. SgEUDO further achieved 39% and 37.5% mean dose reductions in the left and right kidneys, respectively.Significance.Our theoretical and practical refinement of gEUD optimization enables systematic control of dose distribution with reduced inter-planner variability. The combined MgEUDO and SgEUDO strategies provide a generalizable and clinically effective framework for high-precision radiotherapy.