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The purpose of this study was to use an analytical approach to determine the forces in the glenohumeral ligaments during joint motion. Predictions from the analytical approach were validated by comparing them to experimental data. Using a geometric model, the lengths of the four glenohumeral ligaments were determined during anterior-posterior loading simulations and forward flexion-extension. The corresponding force in each structure was subsequently calculated based on length data via load-elongation curves obtained experimentally. During the anterior loading simulation at 0 deg of abduction, the superior glenohumeral ligament carried up to 71 N at the maximally translated position. At 90 deg of abduction, the anterior band of the inferior glenohumeral ligament had the highest force of 45 N during anterior loading. These results correlated well with those found in previous experimental studies. We believe that this validated analytical approach can be used to predict the forces in the glenohumeral ligaments during more complex joint motion as well as assist surgeons during shoulder repair procedures.

Ligament, tendon, and fascia are soft tissues composed primarily of collagen fibers. In ligaments and tendons these fibers are organized into roughly parallel bundles to transmit tensile forces between two bones (ligament) or between muscle and bone (tendon). In tendons the bundles are nearly all oriented along the long axis, whereas in ligaments, typically shorter than tendons, the bundles are also generally organized except for bends and twists at insertion sites to bone, e.g. the anterior cruciate ligament in the knee [1]. Fascia, on the other hand, is a sheet of fibrous tissue which encloses muscle. In the leg, fascia lata encompasses the entire thigh musculature and becomes thicker as it progresses distally [2].

A general continuum model for the nonlinear viscoelastic behavior of soft biological tissues was formulated. This single integral finite strain (SIFS) model describes finite deformation of a nonlinearly viscoelastic material within the context of a three-dimensional model. The specific form describing uniaxial extension was obtained, and the idea of conversion from one material to another (at a microscopic level) was then introduced to model the nonlinear behavior of ligaments and tendons. Conversion allowed different constitutive equations to be used for describing a single ligament or tendon at different strain levels. The model was applied to data from uniaxial extension of younger and older human patellar tendons and canine medial collateral ligaments. Model parameters were determined from curve-fitting stress-strain and stress-relaxation data and used to predict the time-dependent stress generated by cyclic extensions.

The response to a compressive load of a repaired cartilage surface, consisting of full-thickness repair tissue adjacent to normal cartilage, was predicted by the u-p finite element method and compared to that of a normal cartilage surface under the same loading conditions. By individually varying the aggregate modulus, permeability and Poisson's ratio for the repair tissue, analyses were performed to assess the contributions of each to the changes in mechanical behaviour. In comparing the repaired to normal surfaces, the presence of a softer repair tissue resulted in increased axial and decreased radial deformations at any given time point, while a repaired surface with an increased permeability compressed more easily due to the increased fluid flow and caused equilibrium to occur sooner. For smaller Poisson's ratio, the axial deformation was not different from normal if the aggregate modulus was the same as normal; however, the radial expansion was reduced as the repair tissue experienced a larger volume change. These results indicate that the presence of repair tissue in a joint surface can have a strong influence on the mechanical behaviour of the surface.

The ligaments of the knee serve to guide normal joint motion and provide stability. They are composed of densely packed collagen fibers, running parallel to the axis of loading. When unloaded, the tissue has a characteristic crimp pattern. As the ligament is stretched, more collagen fibers are recruited to bear load and the collagen crimp pattern disappears (Viidik and Lewin 1966). This gradual recruitment of ligament fibers results in a nonlinear constitutive relation for the ligament as a whole. During normal activity levels, the ligaments maintain normal knee joint kinematics with relatively small loads. When the knee is subjected to large externally applied forces such as those that occur in sporting activities, excessive joint motion is restricted by the increasing stiffness of the ligament.

In the last decade a number of chemically fixed, soft tissue based bioprostheses have become commercially available. Chemical fixation of these materials changes a number of their physical and chemical properties. Quantitation of these effects has been difficult because of: anisotropy of the biopolymers, variable composition of the materials, and sample size and configuration limitations. Collagen tape, made from reconstituted collagen, has been chosen as a model material because it alleviates many of the aforementioned problems. Its constituent fibers are homogeneous and unidirectional. The cross-sectional area is constant. Thus, the resultant uniaxial tensile stress-strain relationship is reproducible to allow for systematic parametric studies. Results are presented for the change in tensile properties of the collagen tape as a function of exposure time to glutaraldehyde fixative. These properties are described by the equation: sigma = A (eB epsilon-1) The tensile properties of fresh and fixed pericardial tissue were also tested and corroborative results were found.

This investigation presents a new approach in the measurement of the mechanical properties of the ligament substance from tensile testing of a bone-ligament-bone complex. Such basic information should be one of the necessary prerequisites in the evaluation of ligament repair as well as reconstruction by autogenous tissue grafts or artificial ligament implants. The use of a video system permits the determination of tensile strains of the mid-medial collateral ligaments from the canine, swine, and rabbit without mechanically interfering with the ligament deformation during testing. This methodology further eliminates the difficulties of measuring the initial length of the entire medial collateral ligament, as its insertions to bones are ambiguous and cover a large area. It was found that the strain of the ligament substance is consistently and considerably less than specific deformation of the bone-ligament-bone complex. These data suggest that the ligament-bone structure stretches nonuniformly with the highest deformation occurring near or at the ligament insertion sites to bone. Other interesting findings include the variation of tensile strains along the ligament substance for all animal species studied.

Enucleated human eyes, 1–3 days post mortem, were sectioned equatorially and the anterior or posterior segment of the corneoscleral shell was clamped on a metal chamber for pressurization. A flying spot scanner system was used to measure horizontal surface deformations while the pressure in the chamber was changed stepwise. Lateral deformations in directions 90° and 45° to the original horizontal direction were also measured to establish surface isotropy of the material when the eye specimens were pressurized in their natural geometries. The finite element numerical method was then used to construct a mathematical model of the posterior segment of the eye mounted on the metal chamber. This model uses trilinear stress-strain relationships which were adjusted until the predicted surface deformations agreed with the experimental results. Using a similar procedure on the anterior segment, a trilinear stress-strain relation was obtained for the corneal stroma. The trilinear relations were then converted to exponential form by a least square method. The finite element, axisymmetric mathematical model can assign these nonlinear material properties for different portions of the eye and specific variations in geometry such as central corneal or equatorial scleral thinning. Such geometric complexity and material heterogeneity and nonlinearity could not be modeled conveniently by previous mathematical models of the corneoscleral shell. The model will be useful in the analysis of stress and strain in portions of the eye, pressure-volume relations and tonometry.