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We propose Deep-Motion-Net: an end-to-end graph neural network (GNN) architecture that enables 3D (volumetric) organ shape reconstruction from a single in-treatment kV planar X-ray image acquired at any arbitrary projection angle. Estimating and compensating for true anatomical motion during radiotherapy is essential for improving the delivery of planned radiation dose to target volumes while sparing organs-at-risk, and thereby improving the therapeutic ratio. Achieving this using only limited imaging available during irradiation and without the use of surrogate signals or invasive fiducial markers is attractive. The proposed model learns the mesh regression from a patient-specific template and deep features extracted from kV images at arbitrary projection angles. A 2D-CNN encoder extracts image features, and four feature pooling networks fuse these features to the 3D template organ mesh. A ResNet-based graph attention network then deforms the feature-encoded mesh. The model is trained using synthetically generated organ motion instances and corresponding kV images. The latter is generated by deforming a reference CT volume aligned with the template mesh, creating digitally reconstructed radiographs (DRRs) at required projection angles, and DRR-to-kV style transferring with a conditional CycleGAN model. The overall framework was tested quantitatively on synthetic respiratory motion scenarios and qualitatively on in-treatment images acquired over full scan series for liver cancer patients. Overall mean prediction errors for synthetic motion test datasets were 0.16$\pm$0.13 mm, 0.18$\pm$0.19 mm, 0.22$\pm$0.34 mm, and 0.12$\pm$0.11 mm. Mean peak prediction errors were 1.39 mm, 1.99 mm, 3.29 mm, and 1.16 mm.

Generative modelling for shapes is a prerequisite for In-Silico Clinical Trials (ISCTs), which aim to cost-effectively validate medical device interventions using synthetic anatomical shapes, often represented as 3D surface meshes. However, constructing AI models to generate shapes closely resembling the real mesh samples is challenging due to variable vertex counts, connectivities, and the lack of dense vertex-wise correspondences across the training data. Employing graph representations for meshes, we develop a novel unsupervised geometric deep-learning model to establish refinable shape correspondences in a latent space, construct a population-derived atlas and generate realistic synthetic shapes. We additionally extend our proposed base model to a joint shape generative-clustering multi-atlas framework to incorporate further variability and preserve more details in the generated shapes. Experimental results using liver and left-ventricular models demonstrate the approach's applicability to computational medicine, highlighting its suitability for ISCTs through a comparative analysis.