Development of a three-dimensional multibody model of the human knee joint for efficient contact

Abstract

It is known that the osteoarthritis, ligamentous rupture and meniscal tear are the most common knee diseases. These pathologies can cause anomalous contact loads, asymmetrical gait patterns and local pain, which ultimately can lead to a knee arthroplasty. Since there is no standard non-invasive approach to measure in vivo knee loads, knee contact patterns and pressures have to be predicted using computational methods. An efficient methodology to predict knee contact forces, developed under the framework of multibody system (MBS) dynamics, is proposed here. This methodology deals with four main modeling issues: (i) geometrical description of contact surfaces; (ii) contact-impact detection procedure; (iii) constitutive contact force laws; (iv) efficient MBS computational algorithm. The description of the geometry of contacting bodies relies on a parametric surface representation, which can be used to define simple shapes, as spheres, or freeform surfaces, via NURBS. Contact detection consists of evaluating the geometrical requirements that permit to determine the location of the potential contact points, and a penetration condition, that indicates if the bodies are in contact or not. Subsequently, the contact forces are computed based on material and kinematic properties of the bodies. For this purpose, different constitutive contact laws are considered, namely those based on the Hertz contact theory to which a dissipative term is included. The intra-joint contact forces are then added to the equations of motion. Since the description of the contact geometries and the contact-impact detection procedures are very timeconsuming tasks, some modifications have been implemented to a general MBS algorithm and a pre-processing unit is developed, in order to reduce the CPU times and ensure the computational efficiency. Computational simulations using a multibody 3D-model of the human knee joint are performed to validate the proposed approach. The multibody 3D-model is composed by two rigid bodies, femur and tibia, and eight nonlinear springs that represent the knee ligaments. Finally, numerical results obtained from computational simulations are used to discuss the assumptions and procedures adopted in this study.