A phenomenological contact model: Understanding the graft-tunnel interaction in anterior cruciate ligament reconstructive surgery

In this paper, we sought to expand the fidelity of a validated model of the anterior cruciate ligament reconstruction (ACL-R) procedure by incorporating a stick-slip contact model with linear pressure-overclosure relationship at the interface. The suggested model is characterized by three unknown parameters, friction coefficient, shear stress softening and contact stiffness. In the absence of any isolated experiments exploring the graft-tunnel interactions during an aggregate joint load, the calibration data used in this study are derived from a reported biomechanical study. A Bayesian calibration procedure was employed to find the unknown probability distribution function (PDF) of these contact parameters. Initially, the response surface approximations of the predicted graft forces from laxity test simulations was adopted to estimate the likelihood of noisy experimental data reported in the literature. Then, the wide domain of contact parameters was sampled sequentially based on the Marcov Chain Monte Carlo (MCMC) method with acceptance-rejection criteria to search for population of samples in significantly narrower domain of unknown parameters that are associated with the highest occurrence likelihood of noisy experimental data. Our simulations with calibrated contact parameters indicate that pre-tensioning applied at 30° of flexion leads to larger graft force after the joint is fully extended compared to the graft force when the same pre-tensioning force is applied at full extension. Moreover, regardless of the pre-tensioning force, the graft-tunnel contact pressure is larger when the fixation of the graft is performed at full extension, increasing with the pre-tensioning force.