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Large variable deformations of the ligament cannot be adequately quantified by one-dimensional and/or localized measurements. To obtain accurate measurement of non-uniform strains over the entire surface of anterior cruciate ligament (ACL), we used a photoelastic coating technique and a method that allowed us to photograph an ACL around its longitudinal axis. A cadaver knee was modified to expose its ACL for observation, and the ligament was then coated with a photoelastic material. The knee was locked in a jig that allowed simulation of natural knee motion. The jig containing the knee was then mounted on a stand, which allowed the exposed ACL to be photographed from any angle around its longitudinal axis while set at a chosen degree of knee flexion. The jig itself was rotated on its stand so as to obtain a panoramic view of the ACL at a given knee angle. The obtained images of the photoelastic fringe patterns yielded significant information for understanding how the strain distributions along the fiber bundles change in association with knee motion. From the results we obtained using the photoelastic measuring method, we reached the following conclusions. Reciprocal functioning between the anterior and the posterior bundles from extension to flexion of the knee does occur. Strain distribution is not uniform even along the same bundle. The strain behavior of the ACL under uniaxial tensile test does not duplicate the conditions in which the ACL is damaged during knee motion. The differences in strains on the ACL under active and passive knee motions may not be as large as those reported previously in the literature.

In this study, a constitutive equation for the ACL composite was formulated, and 3-D finite deformations and stress distributions of the ACL were calculated using a finite element method to simulate knee flexion. The mathematical model of the ACL was created by a structurally motivated phenomenological approach. It was assumed that the ACL can be ideally represented as a homogeneous hyperelastic matrix (Mooney–Rivin material) in which two families of densely distributed extensible fibers are embedded; the fibers in one family have a parallel orientation, the other fibers extend radially in eight equally spaced directions. The non-linear stress–strain characteristic exhibited by collagen fibers was represented by a tri-linear curve. Simulation was performed and the results provided some original data; the stress distribution within the ACL body as well as that over the surface, the 3-D defeormations and stress distributions of the ACL viewed from other sides in addition to those from the medial side, and the variations of the stress distribution pattern in the ACL which occured when the tibia was displaced anteriorly or posteriorly.

The application of joint contact mechanics requires a precise configuration of the joint surfaces. B-Spline, and NURBS have been widely used to model joint surfaces, but because these formulations use a structured data set provided by a rectangular net first, then a grid, there is a limit to the accuracy of the models they can produce. However new imaging systems such as 3D laser scanners can provide more realistic unstructured data sets. What is needed is a method to manipulate the unstructured data. We created a parametric polynomial function and applied it to unstructured data sets obtained by scanning joint surfaces. We applied our polynomial model to unstructured data sets from an artificial joint, and confirmed that our polynomial produced a smoother and more accurate model than the conventional B-spline method. Next, we applied it to a diarthrodial joint surface containing many ripples, and found that our function's noise filtering characteristics smoothed out existing ripples. Since no formulation was found to be optimal for all applications, we used two formulations to model surfaces with ripples. First, we used our polynomial to describe the global shape of the objective surface. Minute undulations were then specifically approximated with a Fourier series function. Finally, both approximated surfaces were superimposed to reproduce the original surface in a complete fashion.