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

A mechanism for rotation restraints in the knee joint

Ligament function in restraining axial rotation of the tibia relative to the femur cannot be revealed by analysis of ligament forces alone. The action of the articular surfaces should be taken into account as well. In this study: three-dimensional mathematical models of four human knee joints were used to determine the limits of axial rotation between 0 and 90 degrees of flexion, whereby the forces in the ligaments and articular contact were calculated, together with their contribution to the restraint moment that was required to counterbalance the applied axial moment of 3 Nm. In external rotation, the direct axial restraint was provided by the collateral ligaments. In internal rotation, when the cruciate ligaments and medial collateral ligament were predominantly loaded, the direct restraint moment resulting from the ligament forces was not sufficient to counterbalance the applied moment. The articular contact forces, which resulted from balancing the axial components of the ligament forces? contributed considerably to the restraint of internal rotation. Depending on the flexion angle, the contact forces provided approximately 50-85% of the internal restraint, whereas 95-100% of the external rotation restraint was accounted for by the ligament force

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 (+or-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 join

Anatomie und Biomechanik des vorderen Kreuzbandes : ein dreidimensionales Problem

No abstract