The description of the human knee as four-bar linkage.

PURPOSE: We investigate the dependence of the kinematics of the human knee on its anatomy. The idea of describing the kinematics of the knee in the sagittal plane using four-bar linkage is almost as old as kinematics as an independent discipline. We start with a comparison of known four-bar linkage constructions. We then focus on the model by H. Nägerl which is applicable under form closure. METHODS: We use geometry and analysis as the mathematical methods. The relevant geometrical parameters of the knee will be determined on the basis of the dimensions of the four-bar linkage. This leads to a system of nonlinear equations. RESULTS: The four-bar linkage will be calculated from the limits of the constructively accessible parameters by means of a quadratic approximation. CONCLUSIONS: By adapting these requirements to the dimensions of the human knee, it will be possible to obtain valuable indications for the design of an endoprosthesis which imitates the kinematics of the natural knee.

The morphology of the articular surfaces of biological knee joints provides essential guidance for the construction of functional knee endoprostheses.

PURPOSE: In comparative examinations of kinematics of the knees of humans and pigs in flexional/extensional motion under compressive loads, the significant differential geometric essentials of articular guidance are elaborated to criticise the shaping of the articular surfaces of conventional knee-endoprostheses and to suggest constructional outlines that allow the endoprosthesis to adopt natural knee kinematics. Implantation is discussed with regard to the remaining ligamentous apparatus. METHODS: Twelve fresh pig knee joints and 19 preserved human knee joints were moved into several flexional/extensional positions. In each joint, the tibia and femur were repeatably caught by metal plates. After removing all ligaments, the tibia and femur were again caught in these positions, and their points of contact were marked on both articular surfaces. Along the marker points, a thin lead wire was glued onto each surface. The positions and shapes of the four contact lines were mapped by teleradiography. RESULTS: All contact lines were found to be plane curves. The medial and lateral planes were parallel, thus defining the joint's sagittal plane. In the human knee, as compared to the lateral, the medial femoral contact line was always shifted anteriorly by several millimetres. The tibial contact curve was laterally convex and medially concave. In the pig knees, the lateral and medial contact lines were asymmetrically placed. Both tibial curves were convex. CONCLUSIONS: Both knees represent cam mechanisms (with one degree of freedom) that produce rolling of the articular surfaces during the stance phase. Implantation requires preservation of the anterior cruciate ligament, and ligamentous balancing is disadvantageous.

Total knee replacement with natural rollback.

A novel class of total knee replacement (AEQUOS G1) is introduced which features a unique design of the articular surfaces. Based on the anatomy of the human knee and differing from all other prostheses, the lateral tibial "plateau" is convexly curved and the lateral femoral condyle is posteriorly shifted in relation to the medial femoral condyle. Under compressive forces the configuration of the articular surfaces of human knees constrains the relative motion of femur and tibia in flexion/extension. This constrained motion is equivalent to that of a four-bar linkage, the virtual 4 pivots of which are given by the centres of curvature of the articulating surfaces. The dimensions of the four-bar linkage were optimized to the effect that constrained motion of the total knee replacement (TKR) follows the flexional motion of the human knee in close approximation, particularly during gait. In pilot studies lateral X-ray pictures have demonstrated that AEQUOS G1 can feature the natural rollback in vivo. Rollback relieves the load of the patello-femoral joint and minimizes retropatellar pressure. This mechanism should reduce the prevalence of anterior knee pain. The articulating surfaces roll predominantly in the stance phase. Consequently sliding friction is replaced by the lesser rolling friction under load. Producing rollback should minimize material wear due to friction and maximize the lifetime of the prosthesis. To definitely confirm these theses one has to wait for the long term results.

Construction-conditioned rollback in total knee replacement: fluoroscopic results.

Firstly, the way of implementing approximatively the initial rollback of the natural tibiofemoral joint (TFJ) in a total knee replacement (AEQUOS G1 TKR) is discussed. By configuration of the curvatures of the medial and lateral articulating surfaces a cam gear mechanism with positive drive can be installed, which works under force closure of the femoral and tibial surfaces. Briefly the geometric design features in flexion/extension are described and construction-conditioned kinematical and functional properties that arise are discussed. Due to a positive drive of the cam gear under the force closure during the stance phase of gait the articulating surfaces predominantly roll. As a result of rolling, a sliding friction is avoided, thus the resistance to motion is reduced during the stance phase. Secondly, in vivo fluoroscopic measurements of the patella tendon angle during flexion/extension are presented. The patella tendon angle/ knee flexion angle characteristic and the kinematic profile in trend were similar to those observed in the native knee during gait (0°-60°).

Mathematical study on the guidance of the tibiofemoral joint as theoretical background for total knee replacements.

The mathematical approach presented allows main features of kinematics and force transfer in the loaded natural tibiofemoral joint (TFJ) or in loaded knee endoprostheses with asymmetric condyles to be deduced from the spatial curvature morphology of the articulating surfaces. The mathematical considerations provide the theoretical background for the development of total knee replacements (TKR) which closely reproduce biomechanical features of the natural TFJ. The model demonstrates that in flexion/extension such kinematic features as centrodes or slip ratios can be implemented in distinct curvature designs of the contact trajectories in such a way that they conform to the kinematics of the natural TFJ in close approximation. Especially the natural roll back in the stance phase during gait can be reproduced. Any external compressive force system, applied to the TFJ or the TKR, produces two joint reaction forces which--when applying screw theory--represent a force wrench. It consists of a force featuring a distinct spatial location of its line and a torque parallel to it. The dependence of the geometrical configuration of the force wrench on flexion angle, lateral/medial distribution of the joint forces, and design of the slopes of the tuberculum intercondylare is calculated. The mathematical considerations give strong hints about TKR design and show how main biomechanical features of the natural TFJ can be reproduced.