Use of Design of Experiment Approach to Predict Force-Displacement Relationship for the Knee Joint and Menisci in a Multi-Body Dynamic Knee Model

The multi-body method can provide computationally efficient simulations of muscle and tissue interactions. A limitation of the multi-body approach is in the functional representation of soft tissues such as articular cartilage and the menisci. In previous work, a deformable contact with constant coefficients was applied to a subject-specific multi-body knee model to define the contact force between patella, femur, and tibia articular cartilage [1, 2]. Hertzian contact theory was used to determine the parameters of the compliant contact force model based on cartilage material properties and contact geometry. To improve upon the Hertzian theory formulation of contact parameters, a design of experiments approach was used to find prediction equations to determine parameters for a compliant contact and multi-body meniscus model. Solutions for the prediction equations can come from either finite element or experimental solutions.