Physics-informed graph neural network emulation of soft-tissue mechanics

Modern computational soft-tissue mechanics models have the potential to offer unique, patient-specific diagnostic insights. The deployment of such models in clinical settings has been limited however, due to the excessive computational costs incurred when performing mechanical simulations using conventional numerical solvers. An alternative approach to obtaining results in clinically relevant time frames is to make use of a computationally efficient surrogate model, called an emulator, in place of the numerical simulator. In this work, we propose an emulation framework for soft-tissue mechanics which builds on traditional approaches in two ways. Firstly, we use a Graph Neural Network (GNN) to perform emulation. GNNs can naturally handle the unique soft-tissue geometry of a given patient, without requiring any low-order approximations to be made. Secondly, the emulator is trained in a physics-informed manner to minimise a potential energy functional, meaning that no costly numerical simulations are required for training. We present results showing that our framework allows for highly accurate emulation for a range of soft-tissue mechanical models, while making predictions several orders of magnitude more quickly than the simulator.