A kinematic-freedom analysis of a flexed-knee-stance testing rig.

The Oxford Rig was designed for biomechanical testing of post-mortem human knee-joint specimens during simulated flexed-knee stance, such as occurs when riding a bicycle, rising from a chair, or climbing stairs. It has been asserted, but never proven, that the movements of the 'ankle' and 'hip' assemblies of the Oxford Rig combine to allow a knee specimen its natural six degrees-of-freedom of movement (6 d.o.f.). This paper investigates this claim mathematically using the general mobility criterion for spatial linkages and the basics of screw theory. It is shown that within the physiological range of knee-joint movement and the physical construction of the Rig, the knee specimen is allowed full spatial freedom (6 d.o.f.). The general approach used in this paper could also be applied to the analysis and, in particular, to the design of other rigs used for biomechanical testing of post-mortem human joint specimens

Transverse compression of tendons

A study was made of the deformation of tendons when compressed transverse to the fiber-aligned axis. Bovine digital extensor tendons were compression tested between flat rigid plates. The methods included: in situ image-based measurement of tendon cross-sectional shapes, after pre-conditioning but immediately prior to testing; multiple constant-load creep/recovery tests applied to each tendon at increasing loads; and measurements of the resulting tendon displacements in both transverse directions. In these tests, friction resisted axial stretch of the tendon during compression, giving approximately plane strain conditions. This, together with the assumption of a form of anisotropic hyperelastic constitutive model proposed previously for tendon, justified modeling the isochronal response of tendon as that of an isotropic, slightly compressible, neo-Hookean solid. Inverse analysis, using finite element simulations of the experiments and 10 s isochronal creep displacement data, gave values for Young’s modulus and Poisson’s ratio of this solid of 0.31 MPa and 0.49, respectively, for an idealized tendon shape and averaged data for all tendons; and E = 0.14 and 0.10 MPa for two specific tendons using their actual measured geometry. The compression load versus displacement curves, as measured and as simulated, showed varying degrees of stiffening with increasing load. This can be attributed mostly to geometrical changes in tendon cross-section under load, varying according to the initial 3D shape of the tendon

Ligament forces at the knee during isometric quadriceps contractions.

A mathematical model of the knee in the sagittal plane was used to investigate the ligament forces resulting when a posteriorly directed external force, applied to the tibia, resists extension of the knee under increasing isometric quadriceps contractions. The model is based on simple geometric representations of the bones, ligaments and muscles at the knee. An elementary mechanical analysis was used to predict which ligament, the anterior or posterior cruciate, was loaded at a given flexion angle and known line of action of the external force. Ligament force, as a proportion of the external force, was calculated first assuming the ligaments to be represented by single, inextensible lines. Modelling the ligaments as continuous arrays of extensible fibres then showed that tibio-femoral translations and ligament forces increased non-linearly with increasing muscle forces and approached asymptotic values which depended on flexion angle. In most positions of the joint, the calculated asymptotic ligament force values were less than the reported ultimate strength of human ligament, despite quadriceps forces of over three times body weight. The possibility of these asymptotic values of ligament force may explain why, at certain flexion angles, large forces can be developed by the muscles at the knee without ligament rupture

Anteroposterior tibial translation during simulated isometric quadriceps contractions

The anteroposterior tibial translations cause by simulated isometric quadriceps forces of up to 750 N were measured in vitro for two extension-restraining load placements at five flexion angles. Both quadriceps force and tibial translation were flexion-angle and load-placement dependent. Quadriceps force was linearly dependent on restraining force; tibial displacement was either very small (<1 mm) or increased non-linearly with increasing restraining force. The measured directions of tibial translation agreed with the predictions of a sagittal-plane knee model. From the displacement data, the directions and axes of tibial rotation were deduced. © 1995

Injury initiation and progression in the anterior cruciate ligament.

OBJECTIVE: To develop a theoretical model to identify mechanisms by which total and partial tears of the anterior cruciate ligament could occur. DESIGN: A sagittal-plane knee model was used to investigate anterior cruciate ligament injury due to excessive anterior tibial translation. The ligament was modelled as an ordered array of fibres linking femur and tibia. BACKGROUND: Despite years of research, the detailed biomechanics of anterior cruciate ligament injury is not well understood. METHODS: A "critical strain criterion" was used to identify the onset and progression of model ligament fibre disruption. The associated forces were also calculated. RESULTS: At low flexion angles (<20 degrees ), the posterior fibre of the model ligament failed first, and the tear progressed anteriorly through the ligament. At higher flexion angles, the anterior fibre failed first, and the tear progressed posteriorly. Near the flexion angle at which the progression of injury changed direction, all fibres failed at approximately the same anterior tibial translation. At all but very high flexion angles, the force supported by the injured ligament was maximum when initial fibre failure occurred; the force then decreased with increasing anterior tibial translation. CONCLUSIONS: Near (20 degrees ) flexion, all model anterior cruciate ligament fibres fail at approximately the same anterior tibial translation, implying that a partial ligament tear may be impossible in this flexion region. Relevance. This study provides insight into possible mechanisms of initiation and progression of anterior cruciate ligament injury. It suggests that a partial tear of the posterior half of the ligament may be difficult to detect clinically

A model of human knee ligaments in the sagittal plane. Part 1: Response to passive flexion.

The development of a mathematical model of the knee ligaments in the sagittal plane is presented. Essential features of the model are (a) the representation of selected cruciate ligament fibres as isometric links in a kinematic mechanism that controls passive knee flexion and (b) the mapping of all other ligament fibres between attachments on the tibia and femur. Fibres slacken and tighten as the ligament attachment areas on the bones move relative to each other. The model is used to study the shape and fibre length changes of the cruciate and collateral ligaments in response to passive flexion/extension of the knee. The model ligament shape and fibre length changes compare well qualitatively with experimental results reported in the literature. The results suggest that when designing and implanting a ligament replacement with the aim of reproducing the natural fibre strain patterns, the surgeon must not only implant through the natural attachment areas but must also maintain the natural fibre mapping and render all fibres just tight at the appropriate flexion angle