Contact Mechanics of the Human Knee

Methods for Studying Knee Contact Mechanics

In vitro experimental testing protocols incorporating knee simulators, with or without the use of cadavers, are widely used in evaluating kinematics, studying the influence of soft tissues, and analyzing wear and longevity of nonimplanted and implanted knees. Use of knee simulators represent a critical step in the design process of new TKAs. However, the standardized protocols that are used fail to simulate the actual operating conditions, in which considerable intersubject variability exists both in terms of kinematics and kinetics, especially for TKA subjects.

Invasive in vivo experimental techniques, including the use of fracture fixation devices, bone pins, minimally invasive halo ring pin attachments, and roentgen stereophotogrammetric analysis (RSA), have been found to provide high accuracy in kinematic measurements. Noninvasive in vivo methods, however, have superseded invasive techniques in popularity because of obvious ethical concerns. Currently, the most popular methods used for in vivo motion analyses are skin markers and medical imaging. Because of substantial relative movement of the skin over underlying osseous structures, skin marker technology applying suitable correction measures, such as artifact assessment, the point cluster technique, and optimization using minimization, is used extensively when high-speed multibody movement must be tracked. For slow-speed weight-bearing activities, the use of single-plane and bi-plane fluoroscopy or open and closed magnetic resonance imaging (MRI) modalities, coupled with two-dimensional to three-dimensional image registration techniques, have become the gold standards because of the low number of errors associated with these processes.

In vivo force measurements using telemetric knee implants have been reported and have provided invaluable insights into the kinetics of the implanted knee. Because of the high costs involved in its development, telemetry still has not been used on a mass scale. Moreover, this technology is not feasible for studying normal knee joint forces. Therefore, computational modeling has always been a necessity for studying the contact forces occurring at the knee joint. Because the lower limb is connected by many muscles, modeling the knee is inherently indeterminate in nature with more unknowns than equations. Therefore, reduction methods and optimization methods are used to obtain a solution. In the optimization technique, the number of unknowns is greater than the number of equations that can be generated for the solution. Consequently, the process deals with the solution generated by the minimization of a suitably chosen objective function. However, there is still no consensus as to which objective function is physiologically most suitable. With optimization, you might possibly achieve a mathematically correct solution, but it may not be physiologically correct. The reduction technique, on the other hand, uses simplifying assumptions to reduce the complexity of the system. In this case the system remains determinate—that is, the number of unknowns is always made equal to the number of equations that can be generated to solve them. This method, therefore, generates a faster solution when compared with optimization, but only a certain number of unknown variables can be determined.

More recently, computed tomography (CT) and MRI-based techniques have been used to study contact areas and pressures in the normal knee. Contact stress and strain variations are extensively studied using computational techniques. The use of linear and nonlinear finite element analysis with biofidelic models segmented out of CT and MRI scans has been the most popular method for studying behavior in the normal knee and in TKAs. Because TKA components have regular geometry and the contact variation is elliptical in nature, faster contact algorithms using hertz contact, elastic foundation models, modified elastic foundation models, and explicit finite element analysis have also been used. Computational methods have also tried to create virtual wear simulators using adaptive finite elements and elastic foundation models coupled with a damage algorithm.

Normal Knee Motion

The kinematics of the normal knee is complex. The tibiofemoral articulation has six degrees of freedom, but only three of these motions are more dominant in the knee—flexion-extension, internal-external rotation, and anterior-posterior translation. Abduction-adduction, medial-lateral translation, and superior-inferior translation might occur, but are minimal in magnitude compared to the other three motions. At full extension to very early stages of flexion (<10 degrees), the femur is internally rotated with respect to the tibia. In weight-bearing deep knee bend and squatting exercises, with the increase in flexion, the femur starts to roll with slip on the tibia in the posterior direction (posterior femoral rollback) and the femur externally rotates with respect to the tibia ( Fig. 20.1 ). The external rotation of the femur with respect to the tibia with increasing flexion occurs as the lateral condyle moves more posteriorly than the medial condyle. The highest rates of axial rotation have been found to occur from full extension to 30 degrees of flexion. At this flexion range, the medial contact point translates posteriorly, mainly because of the change in the shape of the medial condyle. Above 30 degrees of flexion, the knee enters the active functional arc and the axis of rotation crosses the centers of the almost circular posterior articular surfaces of both femoral condyles. Because the medial collateral ligament is shorter and tighter than the lateral collateral ligament, in this phase, the medial contact point is relatively immobile and moves slightly in both the anterior and posterior direction, allowing the lateral condyle to move considerably posterior relative to the medial condyle. Consequently, the longitudinal rotation of the femur occurs at about an axis passing closer to the medial condyle. At very high ranges of flexion (>140 degrees), thigh-shank contact sets in and influences the tibia to move anteriorly with respect to the femur. This causes both femoral condyles to move considerably posterior with respect to the tibia, and the lateral femoral condyle can reach the posterior edge of the tibial plateau (see Fig. 20.1 ).

Axial rotation of the femur with respect to the tibia is a critical factor in patellofemoral mechanics, allowing the patella to track along the anatomic trochlear groove of the femur. In the normal knee, the patella always maintains contact with the femur. From full extension to 90 degrees of flexion, there is a single region of contact between the femur and patella. However, at flexion angles greater than 90 degrees, the contact areas divide into two separate regions with medial tilting of the patella and contacts with the odd facet at approximately 135 degrees of flexion. The most dominant motion in the patella is its flexion in the sagittal plane, which increases with the flexion of the femorotibial joint. This motion causes the patellofemoral contact locations to travel superiorly with respect to the patella.