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

TL;DR

The paper addresses real-time soft-tissue simulation for digital human twins by introducing a thermodynamics-informed hybrid graph neural network that enforces physical priors via the GENERIC metriplectic formalism. The model blends geometric biases from multi-graph GNNs with open-system port-Hamiltonian structure, using decoders that output energy and entropy gradients along with L and M operators to satisfy thermodynamic constraints. It employs an encoder–processor–decoder pipeline across central liver meshes and actuator graphs, trained on Ogden-Prony material data to produce fast, robust rollouts, achieving forward passes as fast as 1.65 ms and displacement errors below 0.15% with stress errors under 7%. The approach demonstrates strong generalization to unseen anatomies and maintains stability during temporal rollouts, supporting real-time haptic rendering and precision medicine, while highlighting future work on interpretability and scalability of graph-based physics-informed models.

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. 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.

Figures (19)

• Figure 1: Comparison between the main characteristics of numerical methods, hybrid AI, and black box models.
• Figure 2: Graph representations of the unidirected actuator graph, $\mathcal{G}^w$ (in red) and the bidirected central/mesh graph, $\mathcal{G}^m$ (in black). In each graph, $\boldsymbol{v}_i$ represents node attributes, $\boldsymbol{e}_{ij}$ denotes the edge attributes, $\bar{\boldsymbol{u}}_i$ corresponds to external displacements or interactions. Thus, the complete representation of this example would be defined as the superposition of both graphs, forming the multi-graph system $G$.
• Figure 3: Overview of the algorithm block scheme for predicting single-step state variable changes in the vanilla graph framework. (a) The encoder transforms the node and edge features into the latent space. (b) The processor distributes information across the graph using $\mathcal{M}$ message-passing modules. (c) The decoder extracts the gradient vectors from the processed graph. (d) The integrator predicts the state variables for the next time step. This entire sequence is repeated iteratively to generate the system’s dynamic rollout.
• Figure 4: Overview of the algorithm block scheme for predicting single-step state variable changes in the hybrid graph framework. (a) The encoder transforms the node and edge features into the latent space. (b) The processor distributes information across the graph using $\mathcal{M}$ message-passing modules. (c) The decoder extracts the energy and entropy gradients from each node in addition to the flattened operators from each edge. (d) The reparametrization agregates the boundary terms as seen in Eq. (\ref{['eq: Gen12']}) to each node subsystem, predicting a gradient vector based on the GENERIC formulation (e) The integrator predicts the state variables for the next time step. This entire sequence is repeated iteratively to generate the system’s dynamic rollout.
• Figure 5: Overlay of the different hepatic geometries used, along with a projection of the representative contour curves. Every color is associated with a different anatomy, providing a visual representation of the anatomical variability inherent to the database. Image top - meshes. Image bottom - level set curves for each anatomy.