Validation of a three-dimensional model of the knee

Three-dimensional mathematical models of the tibio-femoral joint require input of the geometry of articulating surfaces and ligament insertions, and the mechanical properties of cartilage and ligaments. This paper describes a validation of a knee model through a direct specimen-related comparison between the knee model and the kinematics of four knee joint specimens from which the geometry data were used as input of the model. The knee model is quasi-static and is based on equilibrium of forces and moments. The stiffness properties of the ligaments and articular cartilage were estimated on the basis of data reported in the literature. The so-called reference strains in the ligament bundles for the joint in extension, were determined by using an optimization procedure, minimizing the difference between the kinematics of the model and the kinematics of experimentally obtained flexion motions with an internally or an externally rotated tibia (+/- 3 Nm load). A reasonable to good agreement between the model and the experimental kinematics could be obtained for internal-external rotation laxity and the coupled translations and varus-valgus rotation. The disparity between model and experiment varied from knee to knee, average deviations ranging from close to zero to 8 degrees internal rotation deviation and from 5 mm posterior to 3 mm anterior position deviation. The average anterior-posterior laxities at both 20 degrees and 90 degrees flexion were within the variations reported in the literature, although for each individual joint with some underestimation or overestimation. It was concluded that the optimization procedure compensated for the lack of menisci and capsular structures by higher prestrains, thereby overestimating the ligament forces. Despite the gross simplifications relative to the complex anatomy of the knee, the present knee model can realistically simulate the passive motion characteristics of the human knee joint.