On the Contact Modeling and Analysis of the Human Knee Joint

The goal of this work is to study the influence of the contact force model and contact material properties on the dynamic response of a human knee joint. For this purpose, a multibody knee model composed by two rigid bodies, the femur and the tibia, and four nonlinear spring elements that represent the main knee ligaments, is considered. The contact geometrical profiles are extracted from medical images and fitted using spline functions. The tibia motions are modeled, not using a conventional kinematic joint, but rather in terms of the action of the ligaments and potential contact between the bones. Besides, an external force is applied on the center of mass of the tibia in order to simulate the force of the quadriceps muscle group. When a contact is detected, a continuous contact force law is applied. The contact force laws studied are the Hertz, the Hunt-Crossley and the Lankarani-Nikravesh models. Results obtained from computational simulations show that Hertz law is less suitable to describe the dynamic response of the cartilage contact, because this pure elastic model does not account for the viscoelastic nature of the human articulations. Moreover, the effect of the amplitude of the external applied force on the dynamic response of the knee joint model is also evaluated. The obtained results show that the increase of the amplitude of the external applied force increases the contact indentations and lead to an earlier first impact. As far as to the influence of the material contact properties is concerned, the dynamic response of a healthy and natural knee is analyzed and compared with three pathological and two artificial knee models. Results demonstrate that the presence of the cartilage reduces significantly the knee contact forces.