Thermodynamics-informed graph neural networks for real-time simulation of digital human twins

Abstract The growing importance of real-time simulation in the medical field has exposed the limitations and bottlenecks inherent in the digital representation of complex biological systems. This paper presents a novel methodology aimed at advancing current lines of research in soft tissue simulation. The proposed approach introduces a hybrid model that integrates the geometric bias of graph neural networks with the physical bias derived from the imposition of a metriplectic structure as soft and hard constrains in the architecture, being able to simulate hepatic tissue with dissipative properties. This approach provides an efficient solution capable of generating predictions at high feedback rate while maintaining a remarkable generalization ability for previously unseen anatomies. This makes these features particularly relevant in the context of precision medicine and haptic rendering. Furthermore, this work synthesizes two prominent concepts in recent years: the role of message passing as a geometric mechanism fundamental to graph neural networks, and the potential of thermodynamics-informed networks to enhance extrapolation capabilities beyond training scenarios. We develop a multi-graph interaction between the computational model of the liver and a surgical tool. A displacement imposed at the contact region initiates a controlled flow of information that propagates throughout the graph model, aiming to achieve a steady and more efficient exchange of information across the entire network. The physics bias is obtained by imposing a metriplectic structure, enforced via strong and soft constraints. This ensures that the network satisfies thermodynamic principles during inference, even for a previously unseen system. Based on the adopted methodologies, we propose a model that predicts human liver responses to traction and compression loads in as little as 7.3 milliseconds for optimized configurations and as fast as 1.65 milliseconds in the most efficient cases, all in the forward pass. The model achieves relative position errors below 0.15%, with stress tensor and velocity estimations maintaining relative errors under 7%. This demonstrates the robustness of the approach developed, which is capable of handling diverse load states and anatomies effectively. This work highlights the feasibility of integrating real-time simulation with patient-specific geometries through deep learning, paving the way for more robust digital human twins in medical applications.