Graph-based probabilistic geometric deep learning framework for generation of virtual anatomical populations

In the field of medical imaging, "shape generation" refers to the computational techniques employed to create accurate and detailed representations of anatomical structures/organs. Shape generation plays a crucial role in medical imaging, profoundly impacting clinical applications and diagnostics. Accurate representation of anatomical structures is essential for disease detection, treatment planning, personalized medicine, and computational modelling. Leveraging machine learning and computational modelling opens avenues for valuable insights through In-Silico Clinical Trials (ISCTs). In ISCTs, virtual populations of anatomical shapes are vital for evaluating clinical devices. These populations must capture anatomical and physiological variability while remaining plausible to ensure meaningful and reliable results. By generating virtual shape populations, researchers can simulate and assess medical interventions, accelerating the development of improved therapies and devices. However, constructing generative models faces challenges due to the fact that real-world anatomical shapes, derived from different subjects, exhibit varying topological structures and, in general, there is no topological correspondence among shapes from different subjects. This thesis aims to address the challenges associated with shape matching and generation by introducing an unsupervised probabilistic deep generative model, applicable to datasets including shape surface mesh data with varying topological structures and the absence of correspondences. The proposed framework leverages graph representations to capture the geometric characteristics of anatomical shapes and incorporates advanced techniques in geometric deep learning. By employing these algorithms, the framework is able to establish a learnable set of vertex-wise correspondences between shapes in the latent space while learning/constructing a population-derived atlas model. Subsequently, the model generates virtual populations of anatomical shapes that closely resemble real-world data. This novel generative framework is designed to handle variable mesh topology across patients/input shapes and successfully synthesises anatomically plausible virtual populations with significant variability in shape and diverse topologies. These capabilities expand the potential applications of the approach in computational medicine and make it well-suited for ISCTs.