Integration of a smooth mesh-based contact pressure model into tracking and predictive simulations

Abstract

Musculoskeletal simulations are widely used to estimate joint loading, yet most musculoskeletal models estimate knee contact forces as resultant forces or as normal medial and lateral contact forces, without resolving pressure distributions across the articular surfaces. This paper presents a smoothed mesh-based knee contact pressure model that computes continuously differentiable tibiofemoral contact pressures, enabling its direct integration into full-body movement simulations. Built on an elastic foundation formulation, the model introduces smooth approximations ensuring that all contact functions and their derivatives remain continuous throughout the simulation. A systematic sensitivity analysis was performed across five key parameters: mesh resolution, joint damping and three smoothing parameters. Tracking simulations across eight gait trials demonstrated that the nominal configuration achieved mean RMSE values for medial and lateral knee contact forces of 51.6 N and 75.2 N, respectively, with a mean RMSE for joint angles of 1.45◦ and (r = 0.97), converging in less than three hours on a standard computer. Mesh resolution was identified as the dominant factor that affected both accuracy and convergence, while damping variations had negligible influence. As a proof of concept, the model was also incorporated into predictive simulations, demonstrating that increasing the weight on the contact pressure term in the cost function leads to reduced tibiofemoral loading, particularly in the lateral compartment. The proposed formulation provides a computationally efficient and numerically robust framework for simulating knee contact mechanics within full-body musculoskeletal models. Author summary Knee osteoarthritis is a leading cause of disability worldwide, yet the internal forces acting across the joint during movement are difficult or impossible to measure directly in most individuals. Musculoskeletal simulations offer a powerful alternative, but existing models either oversimplify joint contact into a single resultant force or are too computationally demanding to embed in full-body movement optimizations. We developed a new knee contact model that computes how pressure is distributed across the joint surface in a mathematically smooth and computationally efficient way. This smoothness is crucial, since it enables the model to be used in musculoskeletal simulations with gradient-based solvers and automatic differentiation tools to solve optimal control problems. We validated the model across eight gait trials from a subject with a knee prosthesis, demonstrating accurate reproduction of measured knee contact forces and joint kinematics. We also demonstrated the model’s use in predictive simulations, where penalizing joint pressure in the cost function produced gait adaptations that reduced tibiofemoral loading, particularly in the lateral compartment. This work opens the door to computational tools that can evaluate surgical interventions, assistive devices, and rehabilitation strategies directly in terms of their effect on joint pressure distributions.