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EN
Purpose: The aim of this paper is to develop a model of the patellofemoral joint by considering the linear displacement along axis of cylindrical joint and to use this model in the analysis of the femur spatial displacements caused by the quadriceps muscle force. Method: The linear displacement along the axis of cylindrical joint of the patellofemoral joint is computed using optimization methods – minimization of the difference between the modeled and measured spatial displacements of the femur with respect to the tibia over the full range of the knee flexion. Then, the instantaneous screw displacements of the femur with regard to the tibia and corresponding muscle forces are computed for the model developed. The moment of the force arm with respect to the vector of screw displacement is used to evaluate the effectiveness of the acting force. Results: The simulation results for the model developed show significant improvement of the modeled linear coordinates of the femur reference system with respect to tibia reference system. The displacement analysis of the femur loaded by quadriceps muscle force can be used to describe the patellofemoral dislocation problem. Conclusions: The model of the patella-femur joint where the linear displacement along axis of the cylindrical joint is considered can reproduce the actual patella displacements more accurately. It seems expedient to study elasto-statics problem of this mechanism. The model can be used to study some medical conditions such as patellofemoral dislocation.
EN
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.
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