Articular contact in a three-dimensional model of the knee

This study is aimed at the analysis of articular contact in a three-dimensional mathematical model of the human knee-joint. In particular the effect of articular contact on the passive motion characteristics is assessed in relation to experimentally obtained joint kinematics. Two basically different mathematical contact descriptions were compared for this purpose. One description was for rigid contact and one for deformable contact. The description of deformable contact is based on a simplified theory for contact of a thin elastic layer on a rigid foundation. The articular cartilage was described either as a linear elastic material or as a non-linear elastic material. The contact descriptions were introduced in a mathematical model of the knee. The locations of the ligament insertions and the geometry of the articular surfaces were obtained from a joint specimen of which experimentally determined kinematic data were available, and were used as input for the model. The ligaments were described by non-linear elastic line elements. The mechanical properties of the ligaments and the articular cartilage were derived from literature data. Parametric model evaluations showed that, relative to rigid articular contact, the incorporation of deformable contact did not alter the motion characteristics in a qualitative sense, and that the quantitative changes were small. Variation of the elasticity of the elastic layer revealed that decreasing the surface stiffness caused the ligaments to relax and, as a consequence, increased the joint laxity, particularly for axial rotation. The difference between the linear and the non-linear deformable contact in the knee model was very small for moderate loading conditions. The motion characteristics simulated with the knee model compared very well with the experiments. It is concluded that for simulation of the passive motion characteristics of the knee, the simplified description for contact of a thin linear elastic layer on a rigid foundation is a valid approach when aiming at the study of the motion characteristics for moderate loading conditions. With deformable contact in the knee model, geometric conformity between the surfaces can be modelled as opposed to rigid contact which assumed only point contact