A reciprocal connection factor for assessing knee-joint function

Abstract

In the knee joint, interactions between instantaneous kinetics and kinematics associated with ligamentous and articular tissues are not fully understood. These structures may be represented by the instantaneous screw axis ($) (ISA) and static force vectors ($'). Geometric changes to the joint structure affecting motion have not been fully explained, especially after surgical reconstruction and replacement procedures. The ISA offers a joint-characterisation approach, which is dependent on the combined forces of ligaments, articular contacts and muscles. The standard four-bar linkage model in the sagittal plane demonstrates that the normal contact force and the lines of action of the cruciate ligaments always intersect at the centre of rotation of the joint. A kinematic knee model in which the articular surfaces in the lateral and medial compartments as well as the isometric fascicles in the engaged ligaments may be represented as five constraints in a one-degree-of-freedom parallel spatial mechanism. This study provides a theoretical foundation to elucidate the role of each of these elements in the control of the ISA. A recourse to the principle of virtual work explained through d'Alembert's principle for reducing a dynamics problem to an instantaneous static scenario allows screws to be applied to the biomechanics of human motion. The principle of reciprocity links these approaches together to explain the transmitting load between the tibia and the femur as well as the relative motion within the knee joint. A principal clinical implication of this study is the introduction of the reciprocal connection factor to evaluate knee kinematics and kinetics in one simple term, allowing the quantitative assessment of the outcome of knee-joint treatment and rehabilitation methods.

An Informational Algorithm as the Basis for Perception-Action Control of the Instantaneous Axes of the Knee

“…Screw theory is based on the close relationship between line geometry and spatial kinematics [28]. It has previously been used to characterize knee function [29,30], to explore the effectiveness of the golf swing [31], and as a method of minimizing interference from motion data [31]. Plücker Coordinates [28] were extended here so as to describe screw motion, i.e., the reduction of the displacement of a rigid body to its simplest form, and to locate the IAK in terms of the ISA (Instantaneous Screw Axes).…”

“…As previously described (Kim and Kohles, Kim et al,) [22,29], the forces constraining the movement of the knee joint toward infinitesimal displacement are interlinked in terms of reciprocal conditions. The instantaneous axes of the knee (IAK) are reciprocal to five anatomic constraints: the cruciate ligament (ACL), the posterior cruciate ligament (PCL), the medial collateral ligament (MCL), the lateral collateral ligament (LCL), and the articular contact forces in both the medial (P1) and lateral (P2) compartments of the knee.…”

Tracking Knee Joint Functional Axes through Tikhonov Filtering and Plűcker Coordinates

“…Inverse mechanics equations and the L-curve method were previously applied to estimate the optimal values of the smoothing parameters during multi scale cell-tissue level [11] and joint level [9] biomechanical analyses. A similar technique was applied here to compensate for the STA during the study of joint biomechanics.…”

“…These changes in position and orientation of the KFA should be considered in the analyses of muscle function during human movements (which require moment arms to be defined relative to a functional axis of rotation). In particular, the reciprocal connection theory indicates that the ligaments and cartilage contact contribute to the mechanical constraints within knee joints (Figure 1), which results in a KFA that was also reciprocally connected to the Ground Reaction Forces (GRF) from our view [9]. …”

“…The first aim of the present study was to compensate for the STA by the TRF approach to generate the ISA and correctly locate the KFA. The second aim of our study was to apply the KFA tracking that we obtained, combined with the corresponding GRF tracking as a reciprocal connection, toward the estimation of knee constraint forces for clinical applications [9,10]. We then verify this approach by comparing results obtained in terms of KFA with in vivo knee loads measured directly from an instrumented total knee implant.…”