Modeling long-range dependencies in knee joint contact mechanics: topology diffusion, global routing, and their hybridization.

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. Topology diffusion and global routing capture nonlocal interactions through different structural assumptions; determining whether either mechanism is sufficient, or whether they are complementary, is important for designing mechanically grounded surrogates. 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 generated graph-structured samples for grouped three-fold cross-subject evaluation. Five architectures were compared: standard MeshGraphNet, hierarchical MeshGraphNet, a routing-only transformer, a topology-biased routing transformer, and a hybrid model. The hybrid model performed best overall, reducing RMSE by 20.0% relative to standard MeshGraphNet (0.044 ± 0.005 vs. 0.055 ± 0.008; p = 0.039), while also yielding the lowest peak stress error and the highest spatial agreement for high-risk regions. Standard MeshGraphNet was the strongest non-hybrid model, whereas routing-only strategies were less effective. These findings indicate that topology diffusion provides a robust foundation, while global routing offers complementary gains in reconstructing clinically relevant high-stress patterns.