Characterizing Long-Range Dependencies in Knee Joint Contact Mechanics: A Comparison of Topology Diffusion, Global Routing, and Hybrid Graph Neural Networks

TL;DR

This paper compares different graph neural network architectures, including hybrid models, for surrogate modeling of knee joint contact mechanics, demonstrating that topology diffusion is robust and hybrid models improve high-stress pattern reconstruction.

Contribution

It systematically evaluates topology diffusion, global routing, and hybrid GNNs for knee contact mechanics, highlighting the effectiveness of hybrid models and topology diffusion.

Findings

Hybrid model achieved lowest error and highest spatial agreement.

Topology diffusion alone performed robustly across metrics.

Adding global routing improved high-stress pattern reconstruction.

Abstract

Finite element analysis of knee joint contact mechanics is computationally expensive, which has motivated the development of graph neural network surrogate models. However, effectively representing long-range dependencies in joint mechanical responses remains challenging. This study systematically compared topology diffusion, global routing, and their hybridization for surrogate modeling of knee joint contact mechanics. Using kinematic and force data from nine soccer players performing change-of-direction maneuvers, finite element simulations were used to generate graph-structured samples for training and evaluation under a grouped three-fold cross-subject evaluation framework. Five architectures were compared: standard MeshGraphNet, hierarchical MeshGraphNet, a routing-only transformer, a topology-biased routing transformer, and a hybrid model. The hybrid model achieved the best overall performance, yielding the lowest full-field error and peak stress error, together with the highest spatial agreement for high-risk regions. Among the non-hybrid models, the standard topology-diffusion model performed best overall, whereas routing-only strategies were less effective. These findings indicate that topology diffusion provides a robust basis for surrogate modeling of knee joint contact mechanics within the present benchmark, while the addition of global routing can further improve reconstruction of clinically relevant high-stress patterns.