Validation of mathematical models for the prediction of organs-at-risk dosimetric metrics in high-dose-rate gynecologic interstitial brachytherapy

Purpose: Given the complicated nature of an interstitial gynecologic brachytherapy treatment plan, the use of a quantitative tool to evaluate the quality of the achieved metrics compared to clinical practice would be advantageous. For this purpose, predictive mathematical models to predict the D2_cc of rectum and bladder in interstitial gynecologic brachytherapy are discussed and validated. Methods: Previous plans were used to establish the relationship between D2cc and the overlapping volume of the organ at risk with the targeted area (C0) or a 1-cm expansion of the target area (C1). Three mathematical models were evaluated: D_2cc = α*C1 + β (LIN); D_2cc = α - exp(-β*C₀) (EXP); and a mixed approach (MIX), where both C₀ and C₁ were inputs of the model. The parameters of the models were optimized on a training set of patient data, and the predictive error of each model (predicted D_2cc - real D_2cc) was calculated on a validation set of patient data. The data of 20 patients were used to perform a K-fold cross validation analysis, with K = 2, 4, 6, 8, 10, and 20. Results: MIX was associated with the smallest mean prediction error <6.4% for an 18-patient training set; LIN had an error <8.5%; EXP had an error <8.3%. Best case scenario analysis shows that an error ≤5% can be achieved for a ten-patient training set with MIX, an error ≤7.4% for LIN, and an error ≤6.9% for EXP. The error decreases with the increase in training set size, with the most marked decrease observed for MIX. Conclusions: The MIX model can predict the D_2cc of the organs at risk with an error lower than 5% with a training set of ten patients or greater. The model can be used in the development of quality assurance tools to identify treatment plans with suboptimal sparing of the organs at risk. It can also be used to improve preplanning and in the development of real-time intraoperative planning tools.