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.

Keywords:

• instantaneous screw axis (ISA)
• reciprocal screw
• knee
• reciprocal connection factor
• wrench
• ligaments

Acknowledgements

Financial support by Professor Antonio Veloso of the Faculty of Human Kinetics at the Technical University of Lisbon enabled WK to continue his research on knee biomechanics. Technical resources were facilitated by Professors Gerald Recktenwald and Sung Yi of the Department of Mechanical and Materials Engineering at PSU. Partial support was provided to SSK by the National Institutes of Health (EB007077 and MD003350).