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

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{degrees} 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.