Geometric Deep Learning for Non-Linear Soft Tissue Deformation

by Frederic Bott

Thursday Jan 8, 2026, 2:00 PM → 3:00 PM Europe/Berlin

Seminarraum 413 (IPE)

Final presentation of Frederic Bott's bachelor thesis (physics)

Accurate tumor localization across different imaging modalities is a critical challenge in breast cancer diagnosis and biopsy planning. While Magnetic Resonance Imaging (MRI) is typically performed with the patient in a prone position, X-ray mammography and interventions require significant mechanical compression of the breast. Correlating these geometrically distinct states necessitates complex nonlinear deformation modeling. Conventional Finite Element Method (FEM) offer high physical fidelity but are often too computationally intensive for real-time clinical applications.

This thesis investigates the potential of Graph Neural Networks (GNN) as a fast, data-driven surrogate model to predict node-wise tissue displacement. Three distinct architectures based on the MeshGraphNet framework were implemented and evaluated using a dataset of patient-specific FEM simulations: a Standard MeshGraphNet, a Graph Attention Layer (GAT), and a Physics Constrained model incorporating boundary and volume preservation losses.

The results demonstrate that the Standard MeshGraphNet configuration yields the most robust performance, achieving a Root Mean Squared Error (RMSE) of 2.86 ± 0.63 mm on the test set. This represents an improvement of approximately 39% over existing XGBoost baselines (4.7 mm). Detailed error analysis confirms the model’s scalability across varying breast volumes and tissue types. Conversely, the GAT configuration failed to capture the structural deformation fields effectively. Furthermore, the Physics-Constrained approach revealed a fundamental optimization conflict: static weighting schemes led to ”gradient stiffness”and surface artifacts, resulting in a higher RMSE of 36.7 mm compared to the purely data-driven baseline. These findings establish standard GNNs as a highly promising tool for real-time elastic registration, while highlighting the necessity for adaptive loss balancing in future physics-informed approaches.