Graph Neural Networks (GNNs) have emerged as a powerful tool for analysing non-Euclidean data, such as meshes, which are crucial in medical imaging for modelling anatomical structures. This thesis explores the application of GNNs in shape classification tasks across neuroimaging and cardiac imaging domains, emphasising their potential for computer-aided diagnosis and disease detection. A comparative analysis of convolutional layers and node features demonstrates that Fast Point Feature Histograms (FPFH), a pose-invariant descriptor, significantly enhance GNN performance and generalisation to out-of-distribution data, simplifying preprocessing pipelines by eliminating the need for mesh alignment.

In neuroimaging, biological sex classification serves as a proof-of-concept task, with findings extended to Alzheimer’s disease classification. Further investigations highlight the importance of model inspection to understand feature embeddings and encoded biases, revealing that test accuracy alone is insufficient for model selection. The fusion of imaging and shape features extracted from MRI improves predictive accuracy for clinically relevant tasks such as brain age regression and Alzheimer’s disease classification. Explainability frameworks integrating multi-level insights provide transparency in model decision-making, addressing limitations of existing methods. However, these findings highlight the need for further clinical validation.

The thesis also extends GNN applications to cardiac imaging by automating aortic segmentation and mesh processing pipelines. A proposed deep learning-based registration approach outperforms traditional methods, ensuring high-quality vertex correspondence across meshes while preserving geometric features. Statistical shape analysis using Principal Component Analysis (PCA) quantifies healthy aortic shape variability and identifies correlations between shape modes and demographic or functional parameters.

Overall, this work establishes robust methodologies for leveraging GNNs in medical imaging, offering insights into architectural choices, preprocessing strategies, and interpretability frameworks that advance both neuroimaging and cardiac imaging applications.