Adaptive confidence regions for indirect tracking of moving tumors in radiotherapy

Background Target motion in the course of radiotherapy is one of the largest factors affecting the treatment quality of highly dynamic sites such as lung. A critical component of real-time motion management is not only the prediction of tumor location at a future point in time but assessment of positional uncertainty for the purposes of margin adjustment and optimization of validation schemes. Purpose In this study, we propose to investigate the ability of a confidence estimator to accurately reflect the reliability of individual target position predictions and prospectively detect large prediction errors by relying exclusively on a surrogate signal. Methods This work uses a Bayesian framework for indirect tracking. While constant covariance estimates are commonly used to express the uncertainty of the models involved, in this study new adaptive estimates are derived from the surrogate behavior to reflect increasing uncertainty when the breathing conditions differ from the reference conditions observed during the training step. The accuracy of the resulting 95% predicted confidence regions (CRs) is evaluated on nine breathing sequences involving changes of respiratory types (free, thoracic, abdominal, deep). The breathing motions are collected simultaneously from a lung target and two different surrogate signals (an external marker and an anatomical location within the liver). Receiver operating characteristic (ROC) analysis is performed to evaluate the ability of the predicted uncertainty to prospectively detect large prediction errors. Results Higher CR accuracy is obtained when using the proposed adaptive estimates over using constant estimations: on average over the cohort, the proportion of actual target positions lying within the 95% CR is increased by 40 and 35 p.p. with the internal and external surrogates. The time-dependent inflation of the CR width tends to match the magnitude variation of the prediction errors: the adaptive CR effectively enlarges when the target position cannot be predicted reliably, which corresponds to potentially high prediction errors. More precisely, the ROC analysis indicates that the proposed uncertainty estimate can detect if prediction errors are greater than 5 mm with on average high sensitivity (90%) and modest specificity (54% and 47% from internal and external surrogates, respectively). Conclusions While relying exclusively on the surrogate motion characteristics being continuously monitored, the Bayesian framework coupled to adaptive uncertainty estimations can provide reliable CR able to detect large prediction errors. The findings of this study could be further used to automatically trigger risk management mechanisms prospectively.