How Does the Gradient Measure of the Lung SBRT Treatment Plan Depend on the Tumor Volume and Shape?

PURPOSE: Gradient measure (GM) is a critical index related to normal tissue sparing in radiosurgery. This study aims to describe the dependence of GM on target volume and target shape for lung stereotactic body radiation therapy (SBRT) treatment plans. METHODS: A total of 307 peripheral and 119 central lung SBRT treatment plans were enrolled for this study. A least-squares regression was used for data analysis. First, the equations with different functional forms were established to determine the dependence of GM on a univariaty (V(P) or Sp) and bivariaty (V(P) and Sp), respectively. Then, the correlation coefficients and p-values of variables for all equations were compared and analyzed to determine the dependence of GM on PTV volume (VP) and sphericity (Sp). RESULTS: The power equations had the highest coefficient of determination (R(2)) in the dependence results of GM on univariate V(P). The equations were [Formula: see text] and [Formula: see text] for peripheral and central lesions, respectively. On the other hand, the R(2) of all functional forms were less than 0.25 when the relationship of GM versus univariate Sp was analyzed. Similarly, the power equation also obtained the highest R(2) in bivariaty V(P) and Sp analysis, whether for central or peripheral. However, the R(2) of the bivariate equations were not improved compared with those of univariate equations. Moreover, the p-values of the variable Sp were greater than 0.05. CONCLUSIONS: The GM of the lung SBRT plan is shape-independent and volume-dependent. The dependence of GM on PTV volume for peripheral and central lung cancer can be described by two different power equations. The results of this study can be used as a potential tool to assist dosimetric quality control during the radiosurgery process.