Radiotherapy treatment necessitates accurate tracking of the tumor in real-time, often during free-breathing. However, in lung cancer, the respiration entails a significant displacement of the tumor during radiation. This movement, if not well accounted for, can lead to an under-radiation of the tumor or damaging surrounding healthy regions. It is therefore paramount to be able to follow the displacement of the tumor over the entire respiratory cycle. In deep learning applications, it is important to have enough data to capture reliable and representative motion patterns. However, obtaining large amounts of dynamic images is known to be difficult, especially when there is a need to use manually annotated images. Consequently, even incomplete data are worth being utilized. In this work, we propose a model capable of predicting lungs deformations to predict missing phases in a 4D CT lungs dataset, based on probabilistic motion auto-encoders. The model uses the information from a reference 3D volume obtained at the beginning of treatment and a set of 2D surrogate images to predict the next 3D respiratory volumes. The proposed model was evaluated on a free-breathing 4DCT dataset of 165 patients treated for lung cancer. We achieve a mean performance of 81.70% structural similarity, a mean square error of 3.02% and a negative local cross correlation of 81.43% on a hold-out test set comprised of 34 patients. The proposed model can also be used to complete missing respiratory phases in datasets of 4DCT scans of lungs.
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