The natural tibiofemoral joint (TFJ) functions according to a roll-glide mechanism. In the stance phase (0-20 degrees flexion), the femur rolls backwards over the tibia plateau, while further flexion causes increased gliding. This kinematics is based on the principle of a quadruple joint. The four morphological axes of rotation are the midpoints of the curvatures of the medial and lateral femoral condyles and the medial and lateral tibia plateau. In addition, the medial and lateral compartments are shifted a few millimetres in a sagittal direction, the medial tibia plateau being concave and the lateral plateau convex. In most knee arthroplasties, these factors are not taken into account; instead they are equipped with symmetrical medial and lateral joint surfaces. Thereby, the midpoints of the curvatures of the sagittal contours of the lateral and medial joint surfaces, on the femoral as well as on the tibial sides, create a common axis of rotation which does not allow a physiological roll-glide mechanism. The goal of this study was therefore to report on the biomechanical basis of the natural knee and to describe the development of a novel knee endoprosthesis based on a mathematical model. The design of the structurally new knee joint endoprosthesis has, on the lateral side, a convex shape of the tibial joint surface in a sagittal cross section. Furthermore, from a mathematical point of view, this knee endoprosthesis possesses essential kinematic and static properties similar to those of a physiological TFJ. Within the framework of the authorization tests, the endoprosthesis was examined according to ISO/WC 14243 in a knee simulator. The abrasion rates were, thereby, lower than or at least as good as those for conventional endoprostheses. The presented data demonstrate a novel concept in knee arthroplasty, which still has to be clinically confirmed by long term results.

Wear on total knee replacements is an important criterion for their performance characteristics. Numerical simulations of such wear have seen increasing attention over the last years. They have the potential to be much faster and less expensive than the in vitro tests in use today. While it is unlikely that in silico tests will replace actual physical tests in the foreseeable future, a judicious combination of both approaches can help making both implant design and pre-clinical testing quicker and more cost-effective. The challenge today for the design of simulation methods is to obtain results that convey quantitative information and to do so quickly and reliably. This involves the choice of mathematical models as well as the numerical tools used to solve them. The correctness of the choice can only be validated by comparing with experimental results. In this article, we present finite element simulations of the wear in total knee replacements during the gait cycle standardized in the ISO 14243-1 document, used for compliance testing in several countries. As the ISO 14243-1 standard is precisely defined and publicly available, it can serve as an excellent benchmark for comparison of wear simulation methods. We use comparatively simple wear and material models, but we solve them using a new wear algorithm that combines extrapolation of the geometry changes with a contact algorithm based on nonsmooth multigrid ideas. The contact algorithm works without Lagrange multipliers and penalty parameters, achieving unparalleled stability and efficiency. We compare our simulation results with the experimental data from physical tests using two different actual total knee replacements. Even though the model is simple, we can predict the total mass loss due to wear after 5-million gait cycles, and we observe a good match between the wear patterns seen in experiments and our simulation results. When compared with a state-of-the-art penalty-based solver for the same model, we measure a roughly fivefold increase of execution speed.

Wear on total knee replacements (TKRs) is an important criterion for their performance characteristics. Numerical simulations of such wear has seen increasing attention over the last years. They have the potential to be much faster and less expensive than the in vitro tests in use today. While it is unlikely that in silico tests will replace actual physical tests in the foreseeable future, a judicious combination of both approaches can help making both implant design and pre-clinical testing quicker and more cost-effective.The challenge today for the design of simulation methods is to obtain results that convey quantitative information, and to do so quickly and reliably. This involves the choice of mathematical models as well as the numerical tools used to solve them. The correctness of the choice can only be validated by comparing with experimental results.In this paper we present finite element simulations of the wear in TKRs during the gait cycle standardized in the ISO 14243-1 document, used for compliance testing in several countries. As the ISO 14243-1 standard is precisely defined and publicly available, it can serve as an excellent benchmark for comparison of wear simulation methods. Our novel contact algorithm works without Lagrange multipliers and penalty methods, achieving unparalleled stability and efficiency. We compare our simulation results with the experimental data from physical tests using two different actual TKRs, each test being performed three times. We can closely predict the total mass loss due to wear after five million gait cycles. We also observe a good match between the wear patterns seen in experiments and our simulation results.

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