HyperU-Mesh: Real-time deformation of soft-tissues across variable patient-specific parameters

Physics-based Patient-Specific Biomechanical models (PSBMs), particularly those using finite element methods (FEM), simulate organ behaviors accurately but are computationally intensive, especially for hyper-elastic tissues. To address this, U-Mesh introduced a data-driven approach using U-Net architecture, achieving real-time inference but reliant on precise stiffness knowledge at training. This paper introduces HyperU-Mesh, an extension that integrates a Hypernetwork to condition U-Mesh based on stiffness prior distributions. By training with FEM-simulated data that varies stiffness under a predefined distribution, HyperU-Mesh ensures accuracy across variable stiffness without retraining. Experimental results highlight its effectiveness across different scenarios, showing comparable accuracy to FEM while significantly improving speed.

We aim to estimate the deformation of a PolyDiMethylSiloxane (PDMS) beam under gravity, with the left end fixed to a vertical support. This example, adapted from Mazier et al., involves characterizing the material behavior using the Mach-1™ mechanical testing system (Biomomentum, Canada) for unconfined compression tests. The material is best approximated by a Mooney-Rivlin model with ₁₀ = 101 kPa and ₁₀ = 151 kPa. For validation, we obtained the ground truth deformation data from Mazier et al.

Keywords:

Physics-based biomechanical models, Deep Learning, HyperNetworks.