SU-E-T-379: Concave Approximations of Target Volume Dose Metrics for Intensity- Modulated Radiotherapy Treatment Planning

Abstract

Purpose: The widely used treatment plan metric Dx (mimimum dose to the hottest x% by volume of the target volume) is simple to interpret and use, but is computationally poorly behaved (non-convex), this impedes its use in computationally efficient intensity-modulated radiotherapy (IMRT) treatment planning algorithms. We therefore searched for surrogate metrics that are concave, computationally efficient, and accurately correlated to Dx values in IMRT treatment plans. Methods: To find concave surrogates of D95—and more generally, Dx values with variable x values—we tested equations containing one or two generalized equivalent uniform dose (gEUD) functions. Fits were obtained by varying gEUD ‘a’ parameter values, as well as the linear equation coefficients. Fitting was performed using a dataset of dose-volume histograms from 498 de-identified head and neck IMRT treatment plans. Fit characteristics were tested using a crossvalidation process. Reported root-mean-square error values were averaged over the cross-validation shuffles. Results: As expected, the two-gEUD formula provided a superior fit, compared to the single-gEUD formula. The best approximation uses two gEUD terms: 16.25 x gEUD[a=0.45] – 15.30 x gEUD[a=1.75] – 0.69. The average root-mean-square error on repeated (70/30) cross validation was 0.94 Gy. In addition, a formula was found that reasonably approximates Dx for xmore » between 80% and 96%. Conclusion: A simple concave function using two gEUD terms was found that correlates well with PTV D95s for these head and neck treatment plans. More generally, a formula was found that represents well the Dx for x values from 80% to 96%, thus providing a computationally efficient formula for use in treatment planning optimization. The formula may need to be adjusted for other institutions with different treatment planning protocols. We conclude that the strategy of replacing Dx values with gEUD-based formulas is promising.« less