A three-dimensional mathematical model of the knee-joint

Abstract

A three-dimensional analytical model of the knee-joint is presented, taking into account the geometry of the joint surfaces as well as the geometry and material properties of the ligaments and capsule. The position of a large number of points on the joint surfaces is measured and the geometry of these surfaces is then approximated by polynomials in space. The ligaments and capsule are represented by a number of non-linear springs, with material properties selected from the literature. For a given three-dimensional loading (forces as well as moments) at various flexion-extension angles, the location of contact points, magnitude and direction of contact forces, magnitude of ligament elongation and ligament forces can be calculated. In the results presented in this paper special attention is given to the anterior-posterior laxity of a joint. A sensitivity study was undertaken to evaluate the model response due to some of the model parameters and to gain a better understanding of the function of the elements in the model. It is concluded that the predictions of the model agree well with experiments described in the literature.