A study of constrained models for the kinematic analysis of the human knee joint

In a number of clinical applications such as ligament repair, joint replacement or prosthesis’ design, the understanding of knee kinematics is of fundamental importance. Here, the determination of the joint rotation axes is crucial for the interpretation of joint kinematics. However, concurring definitions of knee joint axes based on anatomic landmarks are in use. Regarding any of these definitions, there is a large variability between observers and different sessions or trials. In order to reduce observer dependence, mathematical procedures based on movement analysis, so-called functional methods, have been developed. Presently, a number of alternative concepts exist allowing for the determination of joint rotation axes [1]. The finite helical axis (FHA) as an invariant description of joint displacements is a powerful tool; however, the FHA is not easy to interpret clinically [2]. Further approaches aim to bridge the gap between clinicians and engineers. The clinical protocol may be conserved while, subsequently, mathematical optimization is employed to reorient the clinically determined rotational axes, aiming at an optimal fit between the data and the underlying kinematic model [3,4]. Therein, the intact human tibio femoral joint (no ligament damage or osteoarthritis) is modeled as a compound hinge joint exhibiting only two rotational axes, flexion/extension (FE) and tibial rotation (TR). It has been shown that, in an angular range of about 40° to 80° of knee flexion during weight bearing flexion exercises, the knee performs an almost plane movement. Furthermore, the flexion range from 0° to 40° is dominated by tibial rotation and flexion [3]. Optimization techniques determine the FE axis in the former angular regime, and the TR axis is found by minimizing the varus-valgus rotation in the latter regime. Here, it is usually assumed that the FE and TR axes are orthogonal and intersect. However, [5] state that the TR axis is anterior to the FE axis and not perpendicular to it. A kinematic model that does not match the natural geometry of the joint is expected to yield unphysical displacements. It is the aim of this contribution to study one particular aspect in detail, namely the effect of an orthogonality constraint when applied to data from a knee exhibiting an arbitrary angle between the rotational axes.